   Chapter 5.CT, Problem 16CT Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

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: MN¯||QR¯

To prove: MNP~QRP

Given figure,

 Statements Reasons 1. ________________2. ∠N≅∠QRP3. _________________4. △MNP~△QRP 1. ___________________2. If 2|| lines are cut by a transversal, ________3. Identity4. _____________________

Proof:

Consider the triangles MNP and QRP,

Given, MN¯||QR¯.

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

Therefore, NQRP

Here, PP (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, PP

NQRP

Therefore, By AA theorem the triangles MNP andQRP are similar

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