2. Proving Triangle Similarity by AA
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What are the values of m∠ L and m∠ X?
No, see solution.
Let's recall the Angle-Angle (AA) Similarity Theorem.
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AA Similarity Theorem |
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If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. |
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Two triangles are similar if and only if all angles of one triangle are congruent to corresponding angles of another triangle. |
Let's check if it is possible for △ JKL and △ XYZ to have three pairs of congruent angles. We are given the sum of the measures of ∠ J and ∠ K, and the sum of the measures of ∠ Y and ∠ Z. m∠ J +m∠ K=85^(∘) and m∠ Y+m∠ Z=80^(∘) Using the Triangle Sum Theorem we can find m∠ L and m∠ X. m∠ L=180^(∘)-85^(∘)=95^(∘) and m∠ X=180^(∘)-80^(∘)=100^(∘) Since m∠ L>80^(∘), triangle △ XYZ does not have an angle congruent to ∠ L. Therefore, △ JKL and △ XYZ cannot have three pairs of congruent angles. It is not possible for these triangles to be similar.