ISEE Upper Level Math : How to find if right triangles are similar

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #3 : Right Triangles

 is a right angle; .

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) and (b) are equal.

Explanation:

. Corresponding angles of similar triangles are congruent, so since  is a right angle, so is 

The hypotenuse  of  is twice as long as leg ; by the  Theorem, . Again, by similiarity, 

.

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