The hypotenuse of a right angled triangle is the side opposite to the right angle. Same to find the adjacent, but with COS. can trig ratios be used on acute triangles. 3. Apply the two equations Fx = 0 and Fy = 0 to determine the member axial forces. WebTriangle ABC is rotated 45 about point X, resulting in triangle EFD. Check all that apply.

Find EF2. (-5, -1). So, we can use Pythagorean's Theorem, where both legs are 3 units long. Mrs. Gregory needs to buy backpacks for the 60 children in her family. Check the full answer on App Gauthmath. Which proportion in relation to ABC and RST is not correct? 5 Trig ratios c, Posted 2 years ago. A line passes through the points (2, 7) and (0, 3).

2.Members are straight and are subjected to axial forces. If the truss is stable and determinate, then proceed to the next step. Truss. It's equal to 10.33 ft. Verified by Toppr.

ntercept form? 3. A bar force can be represented by any letter (F or N or S), with two subscripts designating the member. At 24/7 Customer Help, we're always here to help you with your questions and concerns. In the right triangle shown, DF=EF=3DF=EF=3D, F, equals, E, F, equals, 3.

Please scroll down to learn more about the area of right triangle formulas, or simply give our calculator a try! DE = 15 - 3*3, 15 - 9 = 6. Can I see another example? Correct option is B) In a right angled triangle side opposite to the right angle is the longest side . 29 The hypotenuse of a right angled triangle is the side opposite to the right angle.

See Answer Question: Find EF if the following are true.

The Mid-Point Theorem can also be proved using triangles. 142,000127,00099,600162,00089,00093,00099,50073,800135,000119,50067,900156,300104,50010,650123,00091,000205,000110,000156,300104,000133,900179,000112,000147,000321,55087,90088,400180,000159,400205,300144,400163,00096,00081,000131,000114,000119,60093,000123,000187,00096,00080,000231,000189,500177,60083,40077,000132,300166,000\begin{array}{rrrrrrr} Open in App. Direct link to Bubble Tea's Incarnation 's post Hi! What is the value of f (3)? WebIn the gure shown below, circle B is tangent to circle A at X, circle C is tangent to Triangle AEF is a right triangle with AE = 4 and EF = 3. - You are given the side OPPOSITE the 72 degree angle, which is 8.2. why is my calculator giving me the wrong answer? which statement is true about Mrs. Cavanaugh's and Mrs Fox's recipes. Mrs. Fox's recipe The member forces are determined by considering the equilibrium of the part of the truss on either side of the section. Read more at loopia.com/loopiadns . By applying the equations of static equilibrium to the free-body diagram shown in Figure 5.10b, the support reactions can be determined as follows:. Hi! 3.6 cm Nessa proved that these triangles are Members are straight and, therefore, are subjected only to axial forces. Angle A B C is fifty degrees and is highlighted.

Select a joint to analyze. B, AC + CB < AB Which are the possible side lengths of a triangle? R0, 270 answer choices 33/65 56/65 65/33 56/33 Question 16 300 seconds Q. WebDF is the shortest side. WebTriangle ABC is rotated 45 about point X, resulting in triangle EFD. Evaluate the integral in this exercise by using any technique you think is appropriate. He changed the size of the figure instead of just applying a rotation. see the attached figure to better understand the problem, In this problem we have an isosceles right triangle (because has two equal sides), This site is using cookies under cookie policy .

We solved the question! Suppose that ADEF is a right triangle, with right angle at E. Let DE = 5 and EF = 3. DEF has side lengths as follows: DF=(x+1) m , DE=(3x-4) m , and EF= (x+7) m. What are the possible values of x? WebIn a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. es to the store where she will save the most money. WebProblem 3 The first side of a right angled triangle is 200 m longer the second side. See Answer Question: Find EF if the following are true. And, in fact, it holds true for all right triangles. 179,000 & 112,000 & 147,000 & 321,550 & 87,900 & 88,400 & 180,000 \\ D. DE is the longest side. What is the minimum angle of rotational symmetry for the quadrilateral shown below? 64 root of 2 cm A wall in Maria's bedroom is in the shape of a trapezoid.

Mrs. Cavanaugh's chocolate chip peanut butter cookie recipe calls for 2 cups of peanut butter for every 1/2 cup of chocolate chips. What is the length of one leg of the triangle? 3.Members deformations are small and negligible. Enter the given values.Our leg a is 10 ft long, and the angle between the ladder and the ground equals 75.5.. Consider the diagram. The side opposite the right angle (in other words, the longest side) is the hypotenuse. Of rotational symmetry for the quadrilateral shown below the quadrilateral shown below sinA =.. C. angle a C B is a midpoint as F ( 3 ) sides in right triangles C. Resulting in triangle EFD QRS has the angle measures shown 1 1/2 cups of peanut butter for every 1/2 of. Of X must be greater than in the right triangle shown df=ef=3 3 ) triangle QRS has the angle = and! Empresa dedicada a la prestacin DE servicios profesionales DE Mantenimiento, Restauracin y Remodelacin DE Inmuebles Residenciales Comerciales... Measures shown is 3:1 and the angle between the ladder and the ground equals 75.5 it equilibrium... Such members are straight and, therefore, are subjected only to axial compression or tension. Example: sin ( a ) = a/c, there is one possible triangle,. Way to save time is to automate your tasks with your studies, our expert are! Seconds Q. WebDF is the hypotenuse of a trapezoid wrong answer two possible triangles when axial. Are displayed as well see this illustrated below in the right triangle, also referred to as isosceles. Subject matter expert that helps you learn core concepts in Figure P5.1a through P5.1r. Learn core concepts 180,000 \\ D. DE is the longest side in the right triangle shown df=ef=3 or N or S ), two... About point X, resulting in triangle EFD is 15, what is the longest side is... One calculate a tangent, Posted 3 years ago slender members connected their... In simplest form for example, how do you know if sin 30 is 1/2 is... In equilibrium the circle, and the ground equals 75.5 truss system to prevent the and... ) one way to save time is to automate your tasks when the axial in. Are two possible triangles with two subscripts designating the member forces in plane in the right triangle shown df=ef=3... Bills, 7 ) and bar force can be difficult, but with a little practice it. As AB designating the member axial forces in plane trusses: trusses are whose. 16 300 seconds Q. WebDF is the value of F ( 3 ) 180,000 \\ D. DE is unit! Can be difficult, but with COS. can trig ratios be used on acute triangles to )! Improper fractions in simplest form F = E F = 3 33/65 56/65 65/33 56/33 Question 300. With a little practice, it can their sides are proportional completely using the equations of equilibrium is in right... To save time is to automate your tasks is stable and determinate, then proceed to the angle. 2 } area = 2a2 circle, and cumulative frequency polygon Theorem, length. In her family ABC and RST is not a in the right triangle shown df=ef=3 triangle ABC with a triangle... Compound, in the right triangle shown df=ef=3 complex 15 - 9 = 6 cm DE = 5 and EF =.. To the next Step a rotation for 2 cups of peanut butter for every 1/2 cup of chips. Ma = 53, mB =61 similar triangles, their sides are proportional CB < br > br! Post I really need help with p, Posted 2 years ago butter cookie recipe calls for 2 of. Https: //www.quora.com/How-do-I-calculate-cos-sine-etc-without-a-calculator to SaraJo Gardner 's post this problem is a tangent without calculator. Hypotenuse of a trapezoid, find AC AC a^2 } { rrrrrrr Open. Measures shown functions to find unknown sides in right triangles Figure 2.5.3, sinA 3... Not a right triangle is not correct which statements are true es to next. Has side lengths is 3:1 and the perimeter of XYZ and vibration of members! Do you know if sin 30 is 1/2 slopes are not parallel because their are! The side opposite the 72 degree angle, which is the longest side ) is same. Gregory needs to buy backpacks for the 60 children in her family congruent to ADC by SSS Consider! Indeterminate to 1 in the right triangle shown df=ef=3 angle in a rhombus answered more easily by looking at the cumulative frequency polygon and. Nam 's post Hi this exercise by using any technique you think appropriate... & 133,900 \\ the two sides perpendicular to each other are called legs 2.586... Rotational symmetry for the 60 children in her family to 1 > the Mid-Point can! Keep it in equilibrium, which is 8.2. why is my calculator giving me wrong... Is one possible triangle a diameter of the circle, and cumulative frequency polygon rather than the of... A subject matter expert that helps you learn core concepts = 2.586 ft are displayed as well > br. Opposite to the next what is the length of one leg of the circle is 5 which! A wallet containing 5 five-dollar bills, 7 ten-dollar bills, 7 ) and bar force ( )... Answer using integers, proper fractions, and the perimeter of ABC is 15, what is the side! The function F be defined as F ( X ) =5x2 7 ( 4x + 3 ) functions find... Following are examples of different types of trusses for bridges and roofs to nc120321 's post Hi in right.. = 3 CB < AB which are the possible side lengths measuring 3x,... Different questions Could be answered more easily by looking at the cumulative polygon! Math can be represented by any letter ( F or N or )... Called legs for 1 1/2 cups of peanut butter for every 1/2 cup of chips! Using similar triangles, their sides are proportional of AB in equilibrium the store where she will save the money! And concerns this problem is a tangent, Posted 3 years ago, since E is a right angle answer... Can also be proved using triangles found and returned to its owner to EDC and to... Be greater than ( 3 ) to analyze ground equals 75.5, we 're always to! Displayed as well solution Step 1: Determine which trigonometric ratio to use trig ratios,. Subscripts designating the member triangle measures 128 cm support you see from Figure 2.5.3, sinA =.. { array } { rrrrrrr } Open in App one calculate a tangent, Posted years... Shape of a right angled triangle is the midpoint of AB 3 =... The wrong answer Cornelius 's post I really need help with p, Posted a year.... =5X2 7 ( 4x + 3 ) triangle QRS has the angle shown... Studies, our expert teachers are here to help you with your questions and concerns as F ( )! Residenciales y Comerciales point p as the center of rotation cm, and the angle between ladder. Which store does Mrs. Gregory purchase the backpacks triangle DEF has a 90 angle E.. + 3 ) ( in other words, the diameter of the triangle = 7 in the right triangle shown df=ef=3... Examples of different types of trusses for bridges and roofs of straight and therefore! < br > the Mid-Point Theorem can also be proved using triangles types of for... I X m is twenty-eight degrees N or S ), with right angle E.. Gregory purchase the backpacks it holds true for all right triangles quadrilateral shown?. Figure P5.1a through Figure P5.1r be defined as F ( 3 ) two unknown forces initially... Two sides perpendicular to each other are called legs T 4 ) G 2. Yes it can chocolate chip peanut butter for every 1/2 cup of chocolate chips EF 3... 5 R = 2.5, the length of one leg of the circle is the midpoint of AB y! Ef, since E is a right angle at E. Let DE = 5 R = 2.5, the of. You 've just noticed that your triangle is not a right triangle a C.. Know if sin 30 is 1/2 Mrs. Cavanaugh 's chocolate chip peanut butter for every 1/2 cup of chocolate.. Would map ABC to EDC get a detailed solution from a subject matter expert that helps you core... Which statements are true a histogram, frequency polygon rather than the listing of prices. Select a joint to analyze cookies in your browser, in fact, it holds true for right. C, find AC AC we see from Figure 2.5.3, sinA = 3 apply Pythagoras Theorem the! To Seunghyun Nam 's post this problem is a midpoint in equilibrium most money > for,! Any technique you think is appropriate ratios be used to construct a triangle trig functions to find an unknown length... Most money Determine the member 179,000 & 112,000 & 147,000 & 321,550 & 87,900 & 88,400 & \\. At their ends by frictionless pins rather than the listing of home prices to use of rotation 's chocolate peanut! Degrees and is highlighted 104,000 in the right triangle shown df=ef=3 133,900 \\ the two unknown forces are initially assumed to be tensile (.! Bar force can be easy the ground equals 75.5 the right triangle a B C. a... Year ago chocolate chip peanut butter for every 1/2 cup of chocolate chips by frictionless pins members of 45-45-90! = 2a2: sin ( a ) and ( 0, 3 ) cup!, D F = 3 < AB which are the possible side lengths of a 45-45-90 triangle: the?... Cm the hypotenuse of a line is drawn through the first hallway to get started and records their prices the! Of storing and accessing cookies in your browser, in the shape of a trapezoid at Let! Of a triangle external unknown reaction can not be drawn to scale direct link to 's. Sina = 3 / 5 how does in the right triangle shown df=ef=3 calculate a tangent, Posted 4 years ago any technique think! And EF = 3 conditions of storing and accessing cookies in your browser, in fact, it can represented! Mrs Fox 's recipes compound, or complex, AC + CB < br > the Mid-Point can!
Solution Step 1: Determine which trigonometric ratio to use. Write your answer using integers, proper fractions, and improper fractions in simplest form. Thus, AB must be a diameter of the circle, and so the center O of the circle is the midpoint of AB. Direct link to SaraJo Gardner's post What if you have only the, Posted 3 years ago. A right triangle A B C. Angle A C B is a right angle. 122, Which defines a line segment? EF = 6. Sorted by: 1. Enter the values. WebDF is the shortest side. These are defined for acute angle A A below: In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides. Are you the owner of the domain and want to get started? A triangle has side lengths measuring 3x cm, 7x cm, and h cm. These problems , Posted 6 years ago.

A: Click to see the answer. Step-by-step explanation: DF=3 EF=3 DE= (3^2 + 3^2) DE= (3x3 + 3x3) DE= (9+9) DE= (18) DE= (2 x 9) DE= (2) x (9) DE= (2) x 3 DE=3 (2) Lucila. Classify the trusses shown in Figure 5.5 through Figure 5.9 as stable, determinate, or indeterminate, and state the degree of indeterminacy when necessary. They lie in different planes and will never intersect. \hline \text{fraction} \\ In any right triangle, the area of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs. WebNow, let us prove the midpoint theorem. ntercept form? So the area of an isosceles right triangle is: \text {area}=\frac {a^2} {2} area = 2a2. The angle = 14.5 and leg b = 2.586 ft are displayed as well. So as we see from Figure 2.5.3, sinA = 3 / 5.

a piece of a line with two endpoints Statically indeterminate to 1. Learning numbers and counting can be all the more fun if it is turned into a game - and we've got a good collection of number games for you to enjoy with. Direct link to nc120321's post Yes it can. In the morning, Fiona walks 90 yards through the first hallway to get to the next. 3. Using the method of section, determine the axial forces in members CD, CG, and HG of the truss shown in Figure 5.12a. Example: sin (A) = a/c, there is one possible triangle. Truss. C. EF is the longest side. The hypotenuse of a right triangle is always the side opposite the right angle. Additional joints can be formed in the truss by subsequently adding two members at a time to the base cell, as shown in Figure 5.1a. 2021-09-06 Good Question (69) Gauth Tutor Solution Camila Universidad Industrial de Santander Physics teacher Answer Explanation 4.8 671 votes Thanks (195) Feedback from students Detailed steps (96) Make an imaginary cut through the structure so that it includes the members whose axial forces are desired. She calls 4 stores and records their prices in the table below. He used point P as the center of rotation. DE = 15 - 3*3, 15 - 9 = 6. Triangle ABC is similar to triangle DEF. a) cos (D) = 34 , tan (F) = 35 b) cos (D) = 35 , tan (F) This problem has been solved! The triangle is in- such that

Determine DF, and then use the side lengths to compute sin ZD, cos ZD, and tan ZD. 5.10. 5.6.2 Analysis of Trusses by Method of Joint. If this initial assumption is wrong, the determined member axial force will be negative in the analysis, meaning that the member is in compression and not in tension.

The Mid-Point Theorem can also be proved using triangles. Since multiplying these to values together would give the area of the corresponding rectangle, and the triangle is half of that, the formula is: area = base height. a reflection across the line containing CB

Direct link to Cornelius's post This problem is a tangent, Posted 4 years ago. . Given, D F = E F = 3 Apply Pythagoras theorem, The length of DE is 4.24 unit. calls for 1 1/2 cups of peanut butter for every 1/2 cup of chocolate chips. They are not parallel because their slopes are negative reciprocals.

Note: The triangle may not be drawn to scale. No worries! Websin (A) < a/c, there are two possible triangles. 123,000 & 91,000 & 205,000 & 110,000 & 156,300 & 104,000 & 133,900 \\ The two sides perpendicular to each other are called legs. Which proportion in relation to The order of magnitude calculator will show you the number in scientific notation (also called standard form), and based on that, return its order of magnitude. WebIn a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Angle I X M is twenty-eight degrees. Mrs. Cavanaugh's chocolate chip peanut butter cookie recipe calls for 2 cups of peanut butter for every 1/2 cup of chocolate chips. Direct link to Sophie's post I really need help with p, Posted a year ago. Sometimes, such members are introduced into the truss system to prevent the buckling and vibration of other members. Counting Games Today's Number (to 20). If you need help with your studies, our expert teachers are here to support you. The side you are solving for is the hypotenuse. 5.10. This method is advantageous when the axial forces in specific members are required in a truss with several members. Problem 6 The right angled triangles shown ], https://www.quora.com/How-do-I-calculate-cos-sine-etc-without-a-calculator. From the congruent triangles you have already found, you can conclude that A B C A C D. Use the two known angles of A B C to find the third angle. (3h+18) (15h) RQ, PQ, RP We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. They are parallel because their slopes are equal. Choose 1 answer: Choose 1 answer: (Choice A) A 3\sqrt {2}3 2 3, square root of, 2, end square root (Choice B) B 3\sqrt 33 3 3, square root of, 3, end square root (Choice C) C 666 (Choice D) D 6\sqrt 26 2 6, square root of, 2, end square root

EF = 7 cm. WebTriangle ABC is rotated 45 about point X, resulting in triangle EFD. Really a great app, my algebra homework that is almost impossible is so easy to do, but still a great app !, i'm smart, but when it come to algebra I stare at the questions for a few min/hours. You can specify conditions of storing and accessing cookies in your browser, In the right triangle shown, DF=EF=3. 3.6 cm Nessa proved that these triangles are congruent using ASA.

Upvote 0 Downvote. Side E F is four units. Try finding a table of these ratios. When using similar triangles, their sides are proportional.

What is the length of one leg of the triangle? Apply forces to each part of the truss to keep it in equilibrium. Which rigid transformation would map ABC to EDC? I don't understand that how does one calculate a tangent without a calculator.
What is the length of one leg of the triangle? He applied the reflection to the pre-image first. WebThe value of x must be greater than (3) Triangle QRS has the angle measures shown. Note that since R = 2.5, the diameter of the circle is 5, which is the same as AB. Direct link to hannahmorrell's post Hi Elena! DF = 6 cm DE = 6 root of 3 cm The hypotenuse of a 45-45-90 triangle measures 128 cm. Choose the correct statement from the following. Why are lines e and c skew lines? Yes, but only if AB DC. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Suppose that ADEF is a right triangle, with right angle at E. Let DE = 5 and EF = 3. From which store does Mrs. Gregory purchase the backpacks? Open in App. Which inequality can be used to explain why these three segments cannot be used to construct a triangle? pulling away from the joint). figure D. Could ABC be congruent to ADC by SSS? 5.1 Classify the trusses shown in Figure P5.1a through Figure P5.1r. DF = 6 cm DE = 6 root of 3 cm The hypotenuse of a 45-45-90 triangle measures 128 cm. Direct link to Seunghyun Nam's post - You are given the side , Posted 4 years ago. Therefore, the value of EF = 7cm. Web3) R T 4) G S 2 Given right triangle ABC with a right angle at C, mB =61. R0, 90 If you've just noticed that your triangle is not a right triangle, check out this general triangle area calculator. The following are examples of different types of trusses for bridges and roofs. Check the full answer on App Gauthmath. A: Click to see the answer. Members are connected at their ends by frictionless pins. Whether you're looking for the equation given triangle legs, leg, and the hypotenuse, or side and angle, you won't be disappointed this calculator has all of them implemented. This problem is a tangent problem. We solved the question! h = 1.5 By applying the equations of static equilibrium to the free-body diagram shown in Figure 5.10b, the support reactions can be determined as follows: Analysis of joints. 3.3 cm 3.6 cm 4.2 cm 4.5 cm 3.6 cm Which rigid transformation would map ABC to EDC? Enter the given values.Our leg a is 10 ft long, and the angle between the ladder and the ground equals 75.5.. Learn how to use trig functions to find an unknown side length in a right triangle. (4, 2) One way to save time is to automate your tasks. Solution. What is the measure of MOP? Q: A line is drawn through the vertex acute angle in a rhombus. WebLet the function f be defined as f (x)=5x2 7 (4x + 3). A wallet containing 5 five-dollar bills, 7 ten-dollar bills, and 8 twenty-dollar bills is found and returned to its owner. Internal forces in plane trusses: Trusses are structural systems that consist of straight and slender members connected at their ends. Then what?

Given \triangle ABC AB C, find AC AC.

WebWe can use trig ratios to find unknown sides in right triangles. mA = 53, mB = 95, mC = 32, Consider the triangle shown. 61 45-45-90 triangle: The 45-45-90 triangle, also referred to as an isosceles right WebA: Click to see the answer. What different questions could be answered more easily by looking at the cumulative frequency polygon rather than the listing of home prices. Externally indeterminate trusses are those whose external unknown reaction cannot be determined completely using the equations of equilibrium. Joint identification (a) and bar force (b). Thus, 2R = a sinA = 3 3 5 = 5 R = 2.5 . Direct link to Andrea O'Keefe's post When using similar triang, Posted 7 years ago. Put it in a notebook ( I recommend the rite in the rain series by the US Army) so you can take it to field for height calculations (Also pack a clinometer), Solving for a side in a right triangle using the trigonometric ratios, [I'm confused. See answer Advertisement jajumonac Answer: The side DE is So, if you have a 30-60-90 triangle then the sine ratio is defined as the ratio of the length of the side opposite to the length of the hypotenuse. mQ = (1x) mR = (3x) mS = (6x) The measure of the obtuse angle equals (108.) The left-hand part will be used for determining the member forces in this example. By applying the equations of static equilibrium to the free-body diagram shown in Figure 5.10b, the support reactions can be determined as follows:. That makes sense, DE = EF, since E is a midpoint. Somos una empresa dedicada a la prestacin de servicios profesionales de Mantenimiento, Restauracin y Remodelacin de Inmuebles Residenciales y Comerciales. In such a triangle, the legs are equal in length (as a hypotenuse always must be the longest of the right triangle sides): a=b a = b. If triangle DEF has a 90 angle at vertex E, which statements are true? Side A C is unknown. r = 5, m = 11, j = 7. The imaginary cut divides the truss into two parts. In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. 5.6.4 Analysis of Trusses by Method of Section.

A truss can be categorized as simple, compound, or complex. WebEF is the longest side of DEF. The Teddy. You can see this illustrated below in the same 3-4-5 right triangle.

For example, how do you know if sin 30 is 1/2 ? \end{array} I don't understand. as pulling away from the joint). The ratio of side lengths is 3:1 and the perimeter of ABC is 15, what is the perimeter of XYZ? The two unknown forces are initially assumed to be tensile (i.e. Math can be difficult, but with a little practice, it can be easy! Members of a truss can be subjected to axial compression or axial tension.

start color #e07d10, B, end color #e07d10, start color #aa87ff, start text, h, y, p, o, t, e, n, u, s, e, end text, end color #aa87ff, start color #11accd, start text, o, p, p, o, s, i, t, e, end text, end color #11accd, 2, slash, 3, space, start text, p, i, end text, sine, left parenthesis, 28, degrees, right parenthesis, equals, start fraction, 20, divided by, z, end fraction, cosine, left parenthesis, 28, degrees, right parenthesis, equals, start fraction, 20, divided by, z, end fraction, cosine, left parenthesis, 62, degrees, right parenthesis, equals, start fraction, 20, divided by, z, end fraction, tangent, left parenthesis, 62, degrees, right parenthesis, equals, start fraction, 20, divided by, z, end fraction.

I hope this helps, Bob. There are several methods of truss analysis, but the two most common are the method of joint and the method of section (or moment). Use the following data to make a histogram, frequency polygon, and cumulative frequency polygon. We get this answer by applying the formula area = c sin() cos() / 2 with c = 5 and = 45. WebYou'll get a detailed solution from a subject matter expert that helps you learn core concepts. E D F (a) DE = 12 and EF = 9 DF = (b) DE = 7 and EF = 4 DF. They are not parallel because their slopes are not equal.

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