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

## Example Questions

### Example Question #1 : How To Find If Triangles Are Congruent

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. 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 #2 : How To Find If Triangles Are Congruent

Consider and with .

Which is the greater quantity?

(a) (b) Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

(a) and (b) are equal.

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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