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 :Plane Geometry

Givenandwith

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(a) is greater.

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.

Ssa

Note thatand. The two question marks need to be replaced byand. 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 :Plane Geometry

Considerandwith.

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater.

(a) and (b) are equal.

(a) 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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