Subjects geometry

Triangle Congruence 9E2A9F

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1. The problem asks to identify which shortcut can be used to prove that the given pair of triangles is congruent. 2. The common shortcuts for triangle congruence are: - Side-Angle-Side (SAS): Two sides and the included angle are equal. - Angle-Angle-Side (AAS): Two angles and a non-included side are equal. - Side-Side-Side (SSS): All three sides are equal. - Angle-Side-Angle (ASA): Two angles and the included side are equal. 3. From the description, the triangles share a line segment (a side), and each has a right angle marked near the bottom vertices, indicating two angles are equal (both right angles). 4. Since the triangles share a side and have two equal angles (one right angle each), the congruence can be established by Angle-Side-Angle (ASA) because: - One angle is the right angle in each triangle. - The side they share is common. - The other angle adjacent to the shared side is equal by the mirror image property. 5. Therefore, the correct shortcut is D. Angle-Side-Angle. Final answer: D. Angle-Side-Angle