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Geometry Overlapping Triangles Name: ____________________ In each diagram, the stated triangles are congruent. Identify their common side or angle. 1. BAE ABC 2. SUV WUT Separate and redraw the indicated triangles. Identify any common angles or sides. 3. ACF and AEB 4. FKJ and HJK To start, redraw each triangle separately. Then mark parts congruent that you know are congruent. Complete the drawing to separate the triangles. Then mark parts congruent as before. For 5&6, separate and re-draw the triangles given. Use the given information to mark your separated triangle diagram. Remember overlapping sides/angles. Then, decide if you can justify the congruence statement. 5. ∆𝑈𝑋𝑊: ∆𝑉𝑊𝑋: ̅̅̅̅, ∠𝑼𝑿𝑾 ≅ ∠𝑽𝑾𝑿 Given: ̅̅̅̅̅ 𝑼𝑾 ≅ 𝑽𝑿 Can you justify ∆𝑼𝑿𝑾 ≅ ∆𝑽𝑾𝑿 ? If yes, what is your justification? YES NO 6. ∆𝐾𝐽𝑁: ∆𝐾𝐿𝑀: ̅̅̅̅ ≅ ̅̅̅̅ Given: 𝑲𝑱 𝑲𝑳, ̅̅̅̅̅ 𝑲𝑵 ≅ ̅̅̅̅̅ 𝑲𝑴 Can you justify ∆𝑲𝑱𝑵 ≅ ∆𝑲𝑳𝑴 ? YES NO If yes, what is your justification? Draw the diagram described. 7. Draw a line segment on your paper. Then draw two overlapping, congruent triangles that share the segment as a common side. 8. Draw two right triangles that share a common angle that is not a right angle.