Bella is planning a proof for the Isosceles Triangle Theorem using the following information diagram.Given: APQR is an isosceles triangle with base PRProve: ZP ZRQRFirst, she draws the angle bisector of ZQand labels it QB. She plans to show that ZPand ZR are corresponding parts of congruent triangles. Whichcongruence criterion can be used in her proof to show that APQB 2 ARQB?O ASAO SASO sssO AAS->Ce2$&479.WeyuiSfjk* 00

Answered: Image /qna-images/answer/69b1807b-5a3e-4cc8-b4ae-947e92cd6c82.jpg

Answered: Bella is planning a proof for the…

Bella is planning a proof for the Isosceles Triangle Theorem using the following inlormation diagram. Given: APQRis an isosceles triangle with base PR Prove: ZP 2 ZR Q PZ R

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 30E

See similar textbooks

Related questions

Q: Which of the following are congruent on an isosceles trapezoid? Opposite angles Legs Bases All of…

A: Given that a trapezoid is isosceles trapezoid. We need to find which of the given options are…

Q: Given: AABC is right isosceles. X is the midpoint of AC. AB = BC ty A(0, 2a) Prove: AAXB is…

Q: Given: AABC is an isosceles triangle with vertex angle, ZB. ZA ZE ZBCALDCE BC DC Prove: C is the…

Q: Is ARST similar to AVTU ? 20 R V 15 Yes, SSS- Yes, SAS- These triangles are not similar. Yes, AA~ 6

A: Please refer the attached image for complete solution.

Q: 6. The median to the base of an isosceles triangle is the perpendicular bisector of the base.…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: If C is the unit circle x² + y? = 1 oriented counterclockwise and F (x, y) = xi +y j, what is the…

Q: What theorem can be used to prove these triangles are congruent? A. SAS В. HL C. neither

Q: What additional information is needed in order to prove that the triangles are congruent by the ASA…

A: The Angle – Angle – Side rule (AAS) states that two triangles are congruent if their corresponding…

Q: 15. What theorem would be used to prove the triangles below congruent? V W Y. z- SSS SAS AAA SSA

A: Side angle side (SAS) If two sides and the included angle of one triangle are equal to two sides…

Q: Use Theorem 5.6.1 and the drawing R to complete the proof of this theorem: "If a line is parallel to…

A: Basic proportionality theorem states that a line parallel to one side of a triangle intersects the…

Q: Find a formula for the area of the triangle whose vertices are 0, v, , and v2 in R?. Choose the…

Q: The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection…

A: GivenPQ=QR=RS∴QP & QR are radius of the semicircle PTROB is tangent to semicircle PTR at T&…

Q: In the diagram below, tangent AB and secant ACD are drawn to circle O from an external point A, AB =…

A: Use property of tangent line and secant line

Q: Show that the area of a triangle

Q: 9. If you know that Point M is the midpoint of TS and UR, which of the triangle congruence methods…

A: The solution is :

Q: Which rule explains why these scalene triangles are similar? R 45 90° 50 63 90° F 70 E SAS AA none…

A: Similar triangles

Q: A B D

A: Given query is to find which triangle can be prove congruent using HL theorem.

Q: What additional information is needed in order to prove that the triangles are congruent by the AAS…

A: We have to check

Q: 2. Find the measure of AC if the measure of AOC is 110°. A. 61.5° B. 110°C. 226o D. 270° 3. Given…

Q: In the adjoining figure, O is the centre of a circle. Two equal chords AB and CD intersect at P. If…

A: Given: In the above figure, O is the center of the circle and AB and CD are two equal chords…

Q: For the trapezoid ABCD, E denotes the midpoint of BC. Try to prove that the area of the triangle AED…

Q: Q.5 A b H. a B. Use Pythagoras Theorem on triangles ACH and BCH where, AAC = 90°. %3D Prove that a2…

A: Given The triangle ACH and BCH are right angle triangle .

Q: Consider the incomplete paragraph proof shown. Given: Isosceles AABC with AB BC. Prove: LA LC A D C…

A: Here we have to proof ∠A≅∠C

Q: where ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such…

A: Given: AB = AC <ABP = <ACP

Q: 5. In the accompanying diagram of AAEB, EB is extended to R and K, and mL3 = mL4 = 135. Triangle AEB…

A: In △AEB, it is given that m∠3=m∠4=135∘

Q: ATWX is isosceles, with base WX RY | WX RWXY is an isosceles trapezoid Given: Prove:

A: We have, △TWX is isosceles, with base WX and a line RY↔ such that RY∥WX Since, RY∥WX therefore…

Q: Q 10. What information is needed to prove the triangles below congruent using the SSS Congruence…

Q: 8. Classify the following triangle based on its shape. C O isosceles equilateral scalene O right

Q: State the parts that are needed to prove that the 2 triangles are congruent by the given method.…

A: With W is the midpoint of RP W is the midpoint of XY

Q: In circles and inscribed angles, prove the following theorem. Two Secants Theorem: m/ACE = (AE BD )…

Q: M D G L Suppose TD: SG and MD= SL. What additional information is needed to prove the two triangles…

A: For congruence of triangle on basis of SAS it is necessary that two sides and one angle of triangle…

Q: Complete the table below to prove that the two triangles are similar. If Then: AHEY- Then: AA E Ther

A: In the question it is asked to show the triangles are similar. We have to write the congruency rule…

Q: B E D Which pair of triangles can be established to be congruent to prove that 2DAB = ¿BCD?

A: Two triangle are said to be similar by side Angle side method

Q: YZ is the base of an isosceles triangle; XA || YZ Z1 = 2 Given: Prove: A 2

A: Given: YZ is the base of an isosceles triangle XYZ. YZ is parallel to XA as shown in the given…

Q: In the accompanying figure, ABCD is a trapezoid in which AD|BC and AD> BC. Prove that if AB=CD, then…

A: To prove the given angle

Q: In isosceles trapezoid QRST shown below, QR and TS are bases. R If m2Q = 5x + 3 and mZR = 7x- 15,…

A: Given Isosceles trapezoid QRST Given m∠Q = 5x+3 and m∠R = 7x-15we find m∠T

Q: 4. Identify the following: Trapezoid CARE is an isosceles trapezoid. a. Bases: b. Parallel segments:…

A: 4) Parallel sides of trapezium are called as bases of trapezium . Therefore, a) Bases are AR and CE.…

Q: 9. Given the following equilateral triangle with a circular hole as shown, where would the centroid…

Q: . Let r be the radius of the circle inscribed in a right triangle with legs a and b and hypotenuse…

Q: ABC is a triangle inscribed in a circle. The bisector of ÐBAC cuts BC at X and the circle at Y.…

Q: Given isosceles trapezoid JAYS. ON is the midline. Y J S

Q: Show that the two triangles are similar. Q P v and ZN so ALNQ AMNP.

Q: Given that A = 180 in? of the trapezoid solve for the perimeter. Show your work to prove your…

Q: 7 cm 30 30 7 cm A B D C

A: Topic = Triangles

Q: Where P is the perimeter of a triangle whose inscribed circle has radius length r, the area of the…

A: Where P is the perimeter of a triangle whose inscribed circle has radius length r,the area of the…

Q: In isosceles trapezoid QRST shown below, QR and TS are bases. If mZQ = 5x +3 and mZR = 7x – 15, what…

A: Given that TSRQ is an isosceles trapezoid Properties of isosceles trapezoid both pair of base…

Q: Iskra is a structural engineer, designing a tri-bearing truss for the roof of a new building. She…

A: We are given the following information. So, we have FM≅FI, FR is common, and ∠MFR=∠IFR by the…

Q: Consider trapezoid ABCD with AB || DC. M and N are midpoints of AD and BC, respectively. If AB = 12…

A: Consider the trapezoid as shown in the question. Here, the objective is to find MN

Q: In the diagram below of triangle J KL, M is a midpoint of JK and N is a midpoint of KL. If mZNMK =…

A: From given data ,on solving we get

Q: What additional information is needed in order to prove that the triangles are congruent by the SAS…

A: We have to check

Question

Bella is planning a proof for the Isosceles Triangle Theorem using the following information diagram.
Given: APQR is an isosceles triangle with base PR
Prove: ZP ZR
Q
R
First, she draws the angle bisector of ZQand labels it QB. She plans to show that ZPand ZR are corresponding parts of congruent triangles. Which
congruence criterion can be used in her proof to show that APQB 2 ARQB?
O ASA
O SAS
O sss
O AAS
->
Ce
2$
&
4
7
9.
W
e
y
u
i
S
f
j
k
* 00

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RT
a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter? b Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?
Given: Equiangular RST Prove: RV bisects SRT RVS is a right
What type of trapezoid a has congruent diagonals. b has congruent base angles.
In Exercise 19 to24, complete each proof. Given: WXYZ with diagonals WY and XZ WMXYMZ Prove:
a Are any two regular pentagons similar? b Are any two equiangular pentagons similar?
Prove by the indirect method: Given: Scalene XYZ in which ZW bisects XZY point W lies on XY. Prove: ZW is not perpendicular to XY
Consider regular pentagon RSTVQ not shown. Given that diagonals QT and VR intersect at point F, show that VFFR=TFFQ.
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
Given that rectangle ABCE is similar to rectangle MNPR and that CDEPQR, what can you conclude regarding pentagon ABCDE and pentagon MNPQR?
Given that NP bisects MNQ, state a conclusion involving mMNP and mPNQ.
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.