Question

Identify the similar triangles and explain how the triangles are similar by the Angle- Angle Similarity Theorem

Answer 1

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Answer:

3. ΔQXR ~ ΔYXZ; ∠Q≅∠Y; ∠X≅∠X

4. ΔWXV ~ ΔYXZ; ∠W≅∠Y, ∠WXV≅∠YXZ

Explanation:

3. The right angles are congruent with each other, and the shared angle (X) is congruent with itself. Hence two of the three angles in the triangle are congruent with corresponding angles in the other triangle. The triangle names identify the corresponding vertices.

∠Q≅∠Y; ∠X≅∠X

ΔQXR ~ ΔYXZ

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4. The right angles are congruent with each other, and the vertical angles at X are congruent. Hence two of the three angles in the triangle are congruent with corresponding angles in the other triangle. The triangle names identify the corresponding vertices.

∠W≅∠Y; ∠WXV≅∠YXZ

ΔWXV ~ ΔYXZ