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Chapter 4: Q11. (page 120)

The two triangles shown are congruent. Complete.

a. ΔPAL≅? .

b. PA¯≅?.

c. ∠1≅? because ? .

Then PA¯∥?¯ because ?.

d. ∠2≅?¯ because ?.

Then ?¯∥?¯ because ?.

Short Answer

Expert verified

a. ΔPAL≅ΔRLA¯

b. PA¯≅RA¯.

c. ∠1≅∠3¯ because the corresponding parts of a congruent triangle are also congruent.

Then, PA¯∥RL¯¯because ∠1≅∠3¯

d. ∠2≅∠4¯ because the corresponding parts of a congruent triangle are also congruent.

Then PL¯∥AR¯¯ because∠2≅∠4¯.

Step by step solution

01

Part a. Step 1. Consider the diagram.

Here, the two triangles are congruent.

02

Part a. Step 2. State the explanation.

As, the two triangles are congruent, ΔPAL is congruent to ΔRLA.

03

Part a. Step 3. State the conclusion.

Therefore, ΔPAL≅ΔRLA.

04

Part b. Step 1. Consider the diagram.

Here, the two triangles are congruent.

05

Part b. Step 2. State the explanation.

As ΔPAL≅ΔRLA, the corresponding parts of the congruent tringles are also congruent.

06

Part b. Step 3. State the conclusion.

Therefore, PA¯≅RA¯.

07

Part c. Step 1. Consider the diagram.

Here, the two triangles are congruent.

08

Part c. Step 2. State the explanation.

As ΔPAL≅ΔRLA, the corresponding parts of the congruent tringles are also congruent.

09

Part c. Step 3. State the conclusion.

Therefore, ∠1≅∠3.

As, alternate interior angles ∠1≅∠3are equal, therefore, PA¯is parallel to RL¯.

10

Part d. Step 1. Consider the diagram.

Here, the two triangles are congruent.

11

Part d. Step 2. State the explanation.

AsΔPAL≅ΔRLA, the corresponding parts of the congruent triangles are also congruent.

12

Part d. Step 3. State the conclusion.

Therefore, ∠2≅∠4.

Since, alternate interior angles ∠2≅∠4are equal, thus, PL¯will be parallel to AR¯.

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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 ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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