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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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).

Chapter 5.2, Problem 18E, Quadrilateral ABCD quadrilateral HJKL. If mD=90,AD=8,DC=6, and HL=12, find the length of diagonal HK

To determine

To calculate:

The value of diagonal HK¯.

Explanation

Given:

quadrilateralABCDquadrilateralHJKL.

mD=90,AD=8,DC=6,and HL=12.

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

So, LKDC=HLAD.

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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