Use similar triangles to find CD. A50°40°24B-D.20Figure 21

Answered: A 50° 40° 24 B- D. 20 Figure 21

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.8: The Coordinate Plane

Problem 11E

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Question

Use similar triangles to find CD.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Expert Solution

Solution :

The perpendicular to the hypotenuse will always divide the triangle into two triangle with the same properties as the original triangle.

Thus, the perpendicular AC divides right triangle ABD into two similar triangle ACB and DCA( which are also similar triangle to big triangle ABD).

Now,

In these three triangle the ratio of the corresponding sides will be equal

So,

CD/AC = AC/BC

CD/24 = 24/20

CD = 24×24/20 = 576/20 = 28.8

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