Chapter 5.3, Problem 17E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercises 17 to 24, complete each proof.Given: M N ¯ ⊥ N P ¯ , Q R ¯ ⊥ R P ¯ Prove: Δ M N P ∼ Δ Q R P Exercises 17, 18 PROOF Statements Reasons 1. ? 1. ? 2. ∠ s   N and Q R P are right ∠ s 2. ? 3. ? 3. All right ∠ s are ≅ 4. ∠ P ≅ ∠ P 4. ? 5. ? 5.?

To determine

To complete:

The proof by using given information.

Explanation

Given:

Given: MNÂ¯âŠ¥NPÂ¯,QRÂ¯âŠ¥RPÂ¯

Prove: Î”MNPâˆ¼Î”QRP

 PROOF Statements Reasons 1. ? 1. ? 2. âˆ sâ€‰N and QRP are right âˆ s 2. ? 3. ? 3. All right âˆ s are â‰… 4. âˆ Pâ‰…âˆ P 4. ? 5. ? 5.?

Definition:

AA:

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Description:

Given that MNÂ¯âŠ¥NPÂ¯,QRÂ¯âŠ¥RPÂ¯.

To Prove: Î”MNPâˆ¼Î”QRP

Since two lines MN and NP are perpendicular, they form a right triangle. So that âˆ sâ€‰N and QRP are right âˆ s.

It is known that all right angles are congruent. Therefore, âˆ Nâ‰…âˆ QRP.

The two triangles are MNP and QRP. Both have the common point P

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