How to find if triangles are congruent - ISEE Upper Level (grades 9-12) Quantitative Reasoning

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Question

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

Which is the greater quantity?

(a) $m \angle A$

(b) $m \angle D$

Answer

, 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 $m \angle A = m \angle D$ .

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Question

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

Which is the greater quantity?

(a)

(b)

Answer

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

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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