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Chapter 4: Q2. (page 159)

Given: △MPQ≅△PMN; MS¯≅PR¯.

Prove: △MSN≅△PRQ.

Short Answer

Expert verified

It is given that △MPQ≅△PMN.

Therefore,∠MPQ=∠PMN and PQ=MN.

In the trianglesâ–³MSN and â–³PRQ, it can be noticed that:

∠RPQ=∠SMN

PQ=MN

MS¯≅PR¯

Therefore, the trianglesâ–³MSN andâ–³PRQ are the congruent triangles by using SAS postulate.

Therefore, △MSN≅△PRQ.

Hence proved.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

It is given that △MPQ≅△PMN.

Therefore,∠MPQ=∠PMN and PQ=MN.

03

Step 3. Description of step.

In the trianglesâ–³MSN and â–³PRQ, it can be noticed that:

∠RPQ=∠SMN

PQ=MN

MS¯≅PR¯

Therefore, the trianglesâ–³MSN andâ–³PRQ are the congruent triangles by using SAS postulate.

Therefore, △MSN≅△PRQ.

Hence proved.

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Most popular questions from this chapter

Complete.

A method that can be used to prove right triangles congruent, but cannot be used with other types of triangles, is the?_method.

Write proofs in two–column form.

Given:M is the midpoint of JK¯;∠1≅∠2

Prove:JG¯≅MK¯

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.

The two triangles shown are congruent. Complete.

a. ΔSTO≅? .

b. ∠S≅? because ?.

c. ∠SO≅? because ? .

Then point O is the midpoint of? .

d. ∠T≅? because ?.

Then ST¯∥RK¯because ?.
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