Big Ideas Math Book Geometry Answer Key Chapter 5 Congruent Triangles
Availing and practicing with the BIM Geometry Ch 5 Answer Key at the time of your exam preparation can make you learn the concepts so easily and quickly. You can also clear all your topic doubts by taking the help of Big Ideas Math Geometry Solutions Chapter 5 Congruent Triangles. All these questions and answers are prepared as per the latest syllabus and official guidelines.
Solve the BIM Geometry Ch 5 Congruent Triangles Answer Key provided exercises questions from 5.1 to 5.8, chapter review, chapter test, practices, chapter assessments, etc. Clear all examinations with ease & flying colors.
Exercise 51 Angles Of Triangles
Vocabulary and Core Concept Check
Question 1.Can a right triangle also be obtuse? Explain our reasoning.Answer:
Question 2.COMPLETE THE SENTENCEThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two ____________ interior angles.Answer:The given statement is:The measure of an exterior angle of a triangle is equal to the sum of the measures of the two ____________ interior angles.Hence,The completed form of the given statement is:The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Monitoring Progress and Modeling with Mathematics
In Exercises 3-6, classify the triangle by its sides and by measuring its angles.
Question 3.
The given figure is:We know that,If any side is not equal to each other in the triangle, then the triangle is called a Scalene triangleThe angle greater than 90° is called as Obtuse angleAn angle less than 90° is called an Acute angleHence, from the above,We can conclude that ABC is an Acute scalene triangle
In Exercises 7-10, classify ABC by its sides. Then determine whether it is a right triangle.
Question 7.A, B, Answer:
Question 9.A, B, CAnswer:
We can conclude that the 2 acute angle measures are: 398° and 268°
In Exercises 23-26. find the measure of each acute angle in the right triangle.
Question 23.The measure of one acute angle is 5 times the measure of the other acute angle.Answer:
mA + mB = mACD is proven
Question 45.
Answer:
Lesson 56 Proving Triangle Congruence By Asa And Aas
Monitoring Progress
Question 1.Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.
Answer:WX YZ, XY WZ, and 1 3So, WXY WYZ by the AAS congruence theorem.
Question 2.In the diagram, \ \, \ \, and \ \ . Prove ABC DEF.
Answer:\ \, A DSo, the given information is not enough to prove that ABC DEF.
Question 3.In the diagram, S U and \\ . Prove that RST VYT
Answer:So, the given information is not enough to prove that RST VYT
You May Like: Who Is The Biological Father Of Elton John’s Sons
Lesson 51 Angles Of Triangles
Monitoring Progress
Draw an obtuse isosceles triangle and an acute scalene triangle.Answer:The figures of an obtuse isosceles triangle and an acute triangle are as follows:
Question 2.ABC has vertices A, B, and C, Classify the triangle by its sides. Then determine whether it is a right triangle.Answer:A , B , and C and the triangle is ABCWe know that,To find whether the given triangle is a right-angled triangle or not,We have to prove,AC² = AB² + BC²Where,AC is the distance between A and C pointsAB is the distance between A and B pointsBC is the distance between B and C pointsWe know that,The distance between 2 points = ² + ²Now,Let the given points be considered as A, B, and CSo,AB = ² + ² = 3² + 3²= 9 + 9 = 18BC = ² + ²= ² + 0²AC = ² + ²= ² + 3²
The measure of each acute angle is 90°, 64°, and 26°
Lesson 53 Proving Triangle Congruence By Sas
Monitoring Progress
In the diagram, ABCD is a square with four congruent sides and four rightangles. R, S, T, and U are the midpoints of the sides of ABCD. Also, \ \ and \ \.Question 1.
Answer:Given that,ABCD is a square with four congruent sides and four right angles. R, S, T, and U are the midpoints of the sides of ABCD.So, SV = VU, RS = RU, S = UAll the corresponding sides and angles are congruent. So, SVR UVR.
Question 2.
B = D, S = U, R = T and BS = UD, BR = TD, SR = TUSo, BSR DUT
Question 3.You are designing the window shown in the photo. You want to make DRA congruent to DRG. You design the window so that \ \ and ADR GDR. Use the SAS Congruence Theorem to prove DRA DRG.
Answer:When you rotate DRG 90° towards left, then DRG coincides DRA.so, according to the Side Angle Side Congruence theorem, DRA DRG
Don’t Miss: Who Is Paris Jacksons Mother
Exercise 55 Proving Triangle Congruence By Sss
Vocabulary and Core Concept Check
Question 1.The side opposite the right angle is called the __________of the right triangle.Answer:
Answer:No, the figure has no diagonals. So the figure is not stable.
In Exercises 13 and 14, redraw the triangles so they are side by side with corresponding parts in the same position. Then write a proof.
Question 13.Given \ \\ \\ \Prove BAD CDAAnswer:
Question 14.Given G is the midpoint of \, \ \, E and H are right angles.Prove EFG HIG
EG GH as G is the midpoint of \\ \, E HEFG HIG by SAS congruence theorem.
In Exercises 15 and 16. write a proof.
Question 15.Given \ \, \ \Prove LMJ JKLAnswer:
Question 16.Given \ \, \ \, \ \Prove VWX WVZ
XY YZ, WY VY, WX VZVWX WVZ by SSS Congruence theorem
CONSTRUCTIONIn Exercises 17 and 18, construct a triangle that is congruent to QRS using the SSS Congruence Theorem Theorem 5.8).
Question 17.
Question 18.
Answer:At first, construct a side that is congruent to QS. Draw an arc with the compass with Q as center and radius as QR. Draw another arc that intersects the first arc with S as center and radius as SR. Join the point to Q and S to form a circle that is congruent to QRS.
Question 19.Describe and correct the error in identifying congruent triangles.Answer:
Question 20.ERROR ANALYSISDescribe and correct the error in determining the value of x that makes the triangles congruent.
Answer:
Question 25.A, B, C, D, E, FAnswer:
A, B, C, D, E, F
Answer:
Congruent Triangles Cumulative Assessment
Question 1.Your friend claims that the Exterior Angle Theorem can be used to prove the Triangle Sum Theorem . Is your friend correct? Explain your reasoning.
Answer:Yes
Question 2.Use the steps in the construction to explain how you know that the line through point P is parallel to line m.
Answer:From step 4 the red line is parallel to m and passes through the pint P. So, point P is parallel to line m.
Question 3.The coordinate plane shows JKL and XYZa. Write a composition of transformations that maps JKL to XYZAnswer:The coordinates of J, L K, X, Y, ZJL = ² + ² = 3XZ = ² + ² = 3JK = ² + ² = 5XY = ² + ² = 5KL = ² + ² = 8YZ = ² + ²= 8JK XY, JL XZ, KL YZ
b. Is the composition a congruence transformation? If so, identify all congruent corresponding parts.Answer:JKL XYZ using the SSS Congruence theorem.
Question 4.The directed line segment RS is shown. Point Q is located along \ so that the ratio of RQ to QS is 2 to 3. What are the coordinates of point Q? Q
Read Also: Ksp Chemistry
Lesson 57 Using Congruent Triangles
Monitoring Progress
Explain how you can prove that A C.
Answer:If you can prove that ABD CBD, then A C.AB BC, AD CDBD BD by reflexive property of congruenceSo, ABD CBD by SSS congruence theorem.
Question 2.In Example 2, does it mailer how far from point N you place a stake at point K? Explain.
Answer:
Write a plan to prove that PTU UQP.
Answer:
Describe a situation in which you might choose to use indirect measurement withcongruent triangles to find a measure rather than measuring directly.
Answer:Indirect measurements are calculations based on known lengthsWhen two triangles are similar using AAS, SSS, ASA or SAS indirect measurement can be used to find missing measurements and angles.If you were given a triangle with two angles marked and a similar triangle with two sides marked you would be able to find measurements of the angles indirectly.
Monitoring Progress and Modeling With Mathematics
In Exercise 3-8, explain how to prove that the statement is true.
Question 3.
Answer:QP PT, RP SP, QR STAll pairs of sides are congruent by SSS congruence theorem. QPR STP. Because corresponding parts of congruent triangles are congruent, Q T.
Question 5.\ \Answer:
\ \
Answer:\ \,\ \ by reflexive property of congruenceC BACD BDC by SAS congruence theorem.
Question 7.\ \Answer:
\ \
Answer:VW RT, Q S, W TQVW VRT by the AAS congruence theoremSo, \ \
In Exercises 9-12, write a plan to prove that 1 2.
Question 9.
Congruent Triangles Mathematical Practices
Classify each statement as a definition, a postulate, or a theorem. Explain your reasoning.
Question 1.In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is 1.Answer:The given statement is:In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is 1.We know that,According to the parallel and perpendicular lines theorem, two non-vertical lines are perpendicular if and only if the product of their slopes is -1Hence, from the above,We can conclude that the given statement is a Theorem
Question 2.If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.Answer:The given statement is:If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.We know that,According to the Linear pair perpendicular theorem,When two straight lines intersect at a point and form a linear pair of congruent angles, then the lines are perpendicularHence, from the above,We can conclude that the given statement is a Theorem
Question 3.If two lines intersect to form a right angle. then the lines are perpendicular.Answer:If two lines intersect to form a right angle. then the lines are perpendicular.We know that,According to the Perpendicular lines theorem,When two lines intersect to form a right angle, the lines are perpendicularHence, from the above,We can conclude that the given statement is a Theorem
Don’t Miss: Imagine Math Login
Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles
Guys who are seeking better preparation opportunities can refer to the Big Ideas Math Geometry Answers Chapter 5 Congruent Triangles guide. In this study material, you will find all Ch 5 Congruent Triangles Exercises questions and answers in a detailed explanative way by subject experts. So, get this Big Ideas Math Geometry Answersof Ch 5 Congruent Triangles for free of charge and kickstart your preparation effectively. Also, you can boost up your confidence levels by referring to the Ch 5 BIM Geometry Congruent Triangles Solutions Key.
Congruent Triangles Maintaining Mathematical Proficiency
Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points.
Question 1.P and QAnswer:P , Q We know that,The midpoint M of the segment with the 2 endpoints is:, \ )Let the give points are: and So,By comparing the given poits,We will getx1 = -4, x2 = 0, y1 = 1, y2 = 7Hence,The midpoint M = , \ )= , \ )= Hence, from the above,We can conclude that the midpoint M of the segment with the given endpoints is:
Question 2.G and HAnswer:G , H We know that,The midpoint M of the segment with the 2 endpoints is:, \ )Let the give points are: and So,By comparing the given poits,We will getx1 = 3, x2 = 9, y1 = 6, y2 = -2Hence,The midpoint M = , \ )= , \ )= Hence, from the above,We can conclude that the midpoint M of the segment with the given endpoints is:
Question 3.U and VAnswer:U , V We know that,The midpoint M of the segment with the 2 endpoints is:, \ )Let the give points are: and So,By comparing the given poits,We will getx1 = -1, x2 = 8, y1 = -2, y2 = 0Hence,The midpoint M = , \ )= , \ )= , -1 )Hence, from the above,We can conclude that the midpoint M of the segment with the given endpoints is: , -1 )
Solve the equation.
We can conclude that the value of z is: \
Recommended Reading: What Are Abiotics
Proving Triangle Congruence By Sas
Exploration 1
Work with a partner.
Use dynamic geometry software.a. Construct circles with radii of 2 units and 3 units centered at the origin. Construct a 40° angle with its vertex at the origin. Label the vertex A.Answer:
b. Locate the point where one ray of the angle intersects the smaller circle and label this point B. Locate the point where the other ray of the angle intersects the larger circle and label this point C. Then draw ABC.Answer:
c. Find BC, mB, and mC.Answer:
d. Repeat parts – several times. redrawing the angle indifferent positions. Keep track of your results by copying and completing the table below. What can you conclude?USING TOOLS STRATEGICALLYTo be proficient in math, you need to use technology to help visualize the results of varying assumptions, explore consequences, and compare predictions with data.Answer:
Communicate Your Answer
Question 2.What can you conclude about two triangles when you know that two pairs of corresponding sides and the corresponding included angles are congruent?Answer:
How would you prove your conclusion in Exploration 1?Answer:
Exercise 53 Proving Triangle Congruence By Sas
vocabulary and core concept check
Question 1.What is an included angle?Answer:
Question 2.COMPLETE THE SENTENCEIf two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then __________ .
Answer:If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then two triangles are congruent according to the SAS Congruence Theorem.
Monitoring progress and Modeling with Mathematics
In Exercises 3-8, name the included an1e between the pair of sides given.
Question 3.\ and \Answer:
\ and \
Answer:KLP is the included angle between \ and \
Question 5.\ and \Answer:
\ and \
Answer:KJL is the included angle between \ and \
Question 7.\ and \Answer:
\ and \
Answer:KPL is the included angle between \ and \
In Exercises 9-14, decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem . Explain.
Question 9.
Given \ \, \ \Prove PQT RST
\ \\ \In a parallelogram, diagonals bisect at 90 degrees.PTQ = STR PQT RST
In Exercises 19-22, use the given information to name two triangles that are congruent. Explain your reasoning.
Question 19.SRT URT, and R is the center of the circle.Answer:
ABCD is a square with four congruent sides and four congruent angles.
RSTUV is a regular pentagon.Answer:
Question 23.
Question 25.Describe and correct the error in finding the value of x.Answer:
You May Like: Who Is Generally Recognized As The Founder Of American Psychology
Geometry Unit 7 Similarity Test Answers
Geometry Name _ Chapter 7 Test Geometry Chapter 7 Test Name _ Solve each proportion for x. 1. 10 5 x 14 2 How wide is the county on the map? Find the geometric mean. If the answer is not a whole number, leave it in simplest radical form. Geometry Chapter 7 Similarity Notes. Similar Triangles. Found: 9 Mar 2020 | Rating: 80/100
Chapter 7 Test: Similarity
Play this game to review Geometry. What similarity theorem would prove that these triangles are similar? Preview this quiz on Quizizz. What similarity theorem would prove that these triangles are similar? Chapter 7 Test: Similarity DRAFT. 9th – 12th grade. 38 times. Mathematics. 74% average accuracy. a year ago. … 25 Questions Show answers …
Read Also: Why Are There Different Branches Of Chemistry
Proving Triangle Congruence By Sss
Exploration 1
Work with a partner.Use dynamic geometry software.
a. Construct circles with radii of 2 units and 3 units centered at the origin. Label the origin A. Then draw \ of length 4 units.Answer:
b. Move \ so that B is on the smaller circle and C is on the larger circle. Then draw ABC.Answer:
c. Explain why the side lengths of ABC are 2, 3, and 4 units.Answer:
d. Find mA, mB, and mC.Answer:
e. Repeat parts and several times, moving \ to different locations. Keep track of our results by copying and completing the table below. What can you conclude?USING TOOLS STRATEGICALLYTo be proficient in math, you need to use technology to help visualize the results of varying assumptions, explore consequences, and compare predictions with data.Answer:
QT TR, PQ SR, PT STSo, QPT RST by SSS Congruence Theorem
Determine whether the figure is stable. Explain your reasoning.
Question 4.Answer:The figure is not stable. Because it doesnt have a triangle. By the SSS Congruence Theorem, those triangles cannot change shape.
Question 5.
Answer:The figure is stable as the diagonal forms the triangle. By the SSS Congruence Theorem, these triangles cannot change the shape, so the figure is stable.
Question 6.
Answer:The figure is stable as the diagonal forms the triangle. By the SSS Congruence Theorem, these triangles cannot change the shape, so the figure is stable.
Use the diagram.
Redraw ABC and DCB side by side with corresponding parts in the same position.
Answer:
Proving Triangle Congruence By Asa And Aas
Exploration 1
Determining Whether SSA Is Sufficient
Work with a partner.a. Use dynamic geometry software to construct ABC. Construct the triangle so that vertex B is at the origin. \ has a length of 3 units. and \ has a length of 2 units.Answer:
b. Construct a circle with a radius of 2 units centered at the origin. Locate point D where the circle intersects \. Draw \.Answer:
c. ABC and ABD have two congruent sides and a non included congruent angle.Name them.
d. Is ABC ABD? Explain your reasoning.Answer:
e. Is SSA sufficient to determine whether two triangles are congruent? Explain your reasoning.Answer:
Exploration 2
Determining Valid Congruence Theorems
Work with a partner. Use dynamic geometry software to determine which of the following are valid triangle congruence theorems. For those that are not valid. write a counter example. Explain your reasoning.CONSTRUCTING VIABLE ARGUMENTSTo be proficient in math, you need to recognize and use counterexamples.
| Possible Congruence Theorem |
What information is sufficient to determine whether two triangles are congruent?Answer:
Question 4.Is it possible to show that two triangles are congruent using more than one congruence theorem? If so, give an example.Answer:
Don’t Miss: Geometry Segment Addition Postulate Worksheet