Chapter 4.1, Problem 36E

### 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

# When the bisectors of two consecutive angles of aparallelogram meet at a point on the remaining side,what type of triangle is: a) ∆DEC? b) ∆ADE? c) ∆BCE?

To determine

a.

To find:

The type of the angle in ∆DECwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.

Explanation

Given:

The bisectors of two consecutive angles of the parallelogram ABCD are shown below.

Corollary:

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

In the given parallelogram ABCD.

 PROOF Statements Reasons 1. Parallelogram ABCD 1. Given 2. ADÂ¯âˆ¥BCÂ¯ 2. By the definition of a parallelogram 3. âˆ EDC=âˆ D2 andâˆ DCE=âˆ C2 3. Since DE and CE are angle bisectors of âˆ D and âˆ C 4
To determine

b.

To find:

The type of the angle in ∆ADEwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.

To determine

c.

To find:

The type of the angle in ∆BCEwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.

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