Right triangles similarity please explain step by step Consider the diagram below.580435Determine the values of a, b. and c.

Answered: Consider the diagram beiow. 580 435…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section: Chapter Questions

Problem 18CP

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Right triangles similarity please explain step by step

Consider the diagram below.
580
435
Determine the values of a, b. and c.

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

Step 1

Given right angle tringle:

Geometric Mean Theorems: (Altitude rule)

In right triangle if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, the length of the altitude is the geometric mean of the lengths of the two segments.

$\frac{s e g m e n t}{a l t i t u d e} = \frac{a l t i t u d e}{s e g m e n t}$

The length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

$\frac{d}{a} = \frac{a}{d + c}, \frac{c}{b} = \frac{b}{c + d}$

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