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Chapter 4: Q9. WE (page 137)

For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)

Given:RS¯≅RT¯

Prove:∠3≅∠4

(a)∠3≅∠4

(b)∠3≅∠1;∠2≅∠4

(c)RS¯≅RT¯

(d)∠1≅∠2

Short Answer

Expert verified

Order of the proof isc,d,banda.

Step by step solution

01

Step 1. Apply isosceles triangle theorem.

If the two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

From the figure it can be observed that,RS¯≅RT¯.

Therefore, ∠1≅∠2.

02

Step 2. Vertically opposite angles.

From the figure it can be observed that, ∠1and∠3, ∠2and∠4are vertically opposite angles. Therefore,

∠1≅∠3∠2≅∠4

03

Step 3. Transitive property of congruence.

If∠P≅∠Q and∠Q≅∠S then ∠P≅∠S.

Therefore, ∠3≅∠4.

From the above explanation, the order of proof is c,d,banda.

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Most popular questions from this chapter

The pentagons shown are congruent. Complete.

BLACK≅?¯

State whether the congruence of triangles have the reflexive property, the symmetric property, the transitive property.

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

Find the values of x and y.

29. In ΔJKL,JK¯≅KL¯,m∠J=2x-y,m∠K=2x+2yandm∠L=x+2y
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