Basic Geometry : How to find if right triangles are similar

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #11 : How To Find If Right Triangles Are Similar

Triangles 3

Refer to the above diagram.

True or false: 

Possible Answers:

False

True

Correct answer:

True

Explanation:

The distance from the origin to  is the absolute value of the -coordinate of , which is . Similarly, , and . Also, since the axes intersect at right angles,  and  are both right, and, consequently, congruent. 

According to the Side-Angle-Side Similarity Theorem (SASS), if two sides of a triangle are in proportion to the corresponding sides of a second triangle, and their included angles are congruent, the triangles are similar. 

We can test the proportion statement 

by substituting:

Test the truth of this statement by comparing their cross products:

The cross-products are equal, making the proportion statement true, so two pairs of sides are in proportion. Also, their included angles   and  are congruent. This sets up the conditions of SASS, so .

 

 

Example Question #12 : How To Find If Right Triangles Are Similar

Triangles

Refer to the above figure. 

True, false, or inconclusive: .

Possible Answers:

True

Inconclusive

False

Correct answer:

True

Explanation:

 is an altitude of , so it divides the triangle into two smaller triangles similar to each other - that is, if we match the shorter legs, the longer legs, and the hypotenuses, the similarity statement is

.

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