Chapter 5.CT, Problem 16CT

### 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 16 and 17, complete the statements and reasons in each proof.Given: M N - | | Q R - Prove: △ M N P ~ △ Q R P Statements Reasons 1._______________2. ∠ N ≅ ∠ Q R P 3._______________4. △ M N P ~ △ Q R P 1.____________________2. If 2|| lines are cut by a transversal,________3. Identity4._____________________

To determine

To complete:

The missing statements and reasons.

Explanation

Given: MNÂ¯||QRÂ¯

To prove: â–³MNP~â–³QRP

Given figure,

 Statements Reasons 1. ________________2. âˆ Nâ‰…âˆ QRP3. _________________4. â–³MNP~â–³QRP 1. ___________________2. If 2|| lines are cut by a transversal, ________3. Identity4. _____________________

Proof:

Consider the triangles MNP and QRP,

Given, MNÂ¯||QRÂ¯.

If two parallel lines (MNÂ¯||QRÂ¯) are cut by a transversal, then the corresponding angles are congruent.

Therefore, âˆ Nâ‰…âˆ QRP

Here, âˆ Pâ‰…âˆ P (Identity)

By AA theorem:

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

Here, âˆ Pâ‰…âˆ P

âˆ Nâ‰…âˆ QRP

Therefore, By AA theorem the triangles â–³MNPÂ andâ–³QRP are similar

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