Subjects geometry

Triangle Similarity A968E8

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1. The problem asks to identify the shortcut used to prove that two triangles are similar. 2. The given information shows two triangles sharing a diagonal side and each having a right angle opposite that diagonal. 3. Important similarity shortcuts include: - Angle-Angle (AA): Two angles of one triangle are congruent to two angles of another triangle. - Angle-Side-Angle (ASA): Two angles and the included side are congruent. - Side-Side-Side (SSS): All three sides are proportional. - Side-Angle-Side (SAS): Two sides and the included angle are proportional/congruent. 4. Since both triangles have a right angle (one angle congruent) and they share the diagonal side (common side), the other angle adjacent to the diagonal is also congruent because the two right angles are opposite the diagonal. 5. Therefore, the two triangles have two pairs of congruent angles, satisfying the Angle-Angle (AA) similarity criterion. 6. Hence, the shortcut to prove similarity is Angle-Angle Similarity. Final answer: A. Angle-Angle Similarity