How to find if triangles are congruent

ISEE Upper Level Quantitative Reasoning · Learn by Concept

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ISEE Upper Level Quantitative Reasoning › How to find if triangles are congruent

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1

Consider $\Delta ABC$ and $\Delta DEF$ with .

Which is the greater quantity?

(a) $m \angle A$

(b) $m \angle D$

(a) and (b) are equal.

CORRECT

(a) is greater.

0

(b) is greater.

0

It is impossible to tell from the information given.

0

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,

$\Delta ABC \cong \Delta DEF$ .

Corresponding angles of congruent sides are congruent, so $m \angle A = m \angle D$ .

2

Given $\Delta ABC$ and $\Delta DEF$ with $AC = DF, AB = DE, m \angle B = m \angle E$

Which is the greater quantity?

(a)

(b)

It is impossible to tell from the information given.

CORRECT

(a) is greater.

0

(b) is greater.

0

(a) and (b) are equal.

0

Explanation

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

Ssa

Note that and $m \angle B = m \angle E$ . 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.

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