   Chapter 5.2, Problem 18E 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

Quadrilateral A B C D ∼ quadrilateral H J K L . If m ∠ D = 90 ∘ , A D = 8 , D C = 6 , and H L = 12 , find the length of diagonal H K ¯ (not shown). To determine

To calculate:

The value of diagonal HK¯.

Explanation

Given:

Concept Used:

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

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.

Pythagoras Theorem:

It states that sum of the length of the two sides is equal to the square of the length of the hypotenuse (longest sides).

(Hypotenuse)2=(Base)2+(Perpendicular)2

Calculation:

According to the definition of similar polygon, AH,BJ,DL,and CK

Substitute the value of LK,DC,HL and AD in an above equation, we get

LK6=128LK=1268=9

It is given that mD=90

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