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) (a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

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) (a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

(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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