ISEE Upper Level Quantitative : How to find if triangles are congruent

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

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Example Questions

Example Question #13 : Acute / Obtuse Triangles

Given  and  with 

Which is the greater quantity? 

(a) 

(b) 

Possible Answers:

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

It is impossible to tell from the information given.

Explanation:

Examine the diagram below, in which two triangles matching the given descriptions have been superimposed.

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Note that  and . The two question marks need to be replaced by  and . No matter how you place these two points, . However, with one replacement, ; with the other replacement, . Therefore, the information given is insufficient to answer the question.

Example Question #14 : Acute / Obtuse Triangles

Consider  and  with .

Which is the greater quantity? 

(a) 

(b) 

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

, so, by the Side-Side-Side Principle, since there are three pairs of congruent corresponding sides between the triangles, we can say they are congruent - that is,

.

Corresponding angles of congruent sides are congruent, so .

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