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Chapter 4: Q13. (page 132)

Given: RS炉鈯�planeY;鈭�TRS鈮�鈭�VRS

Prove: 螖RTVis isosceles.

Short Answer

Expert verified

Statement

Reason

1.鈭�TRS鈮�鈭�VRS

Given

2.RS炉鈮�RS炉

Reflexive property

3.m鈭�RST=m鈭�RSV=90掳

From given

4.螖UWX鈮�螖VWX

ASA Congruency rule

5.RT炉鈮�RV炉

corresponding parts of congruent triangles are congruent

6.螖RTV is an isosceles triangle

Definition of isosceles triangles

Step by step solution

01

Step 1. Show that ΔRST≅ΔRSV.

By reflexive property of congruence,a side is congruent to itself

So,RS炉鈮�RS炉

Also using given m鈭�RST=m鈭�RSV=90掳

Thus,螖UWX鈮�螖VWX by ASA (Angle-Side-Angle) congruency criteria

02

Step 2. Show that RT¯≅RV¯.

Since, corresponding parts of congruent triangles are congruent

So, RT炉鈮�RV炉

03

Step 3. Show that  is isosceles.

By definition of isosceles triangles, a triangle is isosceles if two sides are congruent.

SinceRT炉鈮�RV炉

Thus螖RTV is an isosceles triangle.

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

OR炉is a common side of two congruent quadrilaterals.

Complete: quad. NERO鈮�quad ?炉.

Plot the given points on graph paper. Draw 螖ABCand 螖DEF. Copy and complete the statement 螖ABC鈮�?炉.

A鈭�1,2B4,2C2,4

D5,鈭�1E7,1F10,鈭�1

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.
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