Chapter 5.2, Problem 20E

### 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

# Quadrilateral A B C D ∼ quadrilateral H J K L . If m ∠ A = m ∠ K = 70 , ∘ and m ∠ B = 110 ∘ , .What types of quadrilaterals are A B C D H J K L ?

To determine

The types of quadrilateral of ABCD and HJKL.

Explanation

Given:

mâˆ A=mâˆ K=70âˆ˜,andÂ mâˆ B=110âˆ˜.

Definition Used:

The sum of measure of angle in a quadrilateral is 360âˆ˜.

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

Calculation:

According to the definition of similar polygon, âˆ Aâ†”âˆ H,âˆ Bâ†”âˆ J,âˆ Dâ†”âˆ L,â€‰andÂ âˆ Câ†”âˆ K

Here, congruent angles are of same measure.

mâˆ C=mâˆ K=70âˆ˜mâˆ J=mâˆ B=110âˆ˜mâˆ H=mâˆ A=70âˆ˜

mâˆ A+mâˆ B+mâˆ C+mâˆ D=360âˆ˜

Substitute the value of mâˆ A,mâˆ B,andÂ mâˆ C in an above equation, we get

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