Mathematics, 14.12.2021 19:40 anyar

Given ABCD is a rectangle. Which of the following proves △EAD≅△EBC? A. 1. ABCD is a rectangle. (Given)
2. ∠A and ∠B are right angles.(Def. of rectangle)
3. ∠A≅∠B (Rt. ∠s ≅ Thm.)
4. ABCD is a parallelogram.(Rectangle→parallelog ram)
5. AD¯¯¯¯¯≅BC¯¯¯¯¯(Parallelogram→opp. sides ≅)
6. EA¯¯¯¯¯≅EB¯¯¯¯¯ (Given)
7. △EAD≅ △EBC (SAS Steps 3, 5, 6)

B. 1. ABCD is a rectangle. (Given)
2. ABCD is a parallelogram.(Rectangle→parallelog ram)
3. ∠A≅∠B (Same-side Int. ∠s Thm.)
4. AD¯¯¯¯¯≅BC¯¯¯¯¯(Parallelogram→opp. sides ≅)
5. AB¯¯¯¯¯≅DC¯¯¯¯¯(Parallelogram→opp. sides ≅)
6. EA¯¯¯¯¯≅EB¯¯¯¯¯ (Given)
7. △EAD≅ △EBC (SAS Steps 3, 5, 6)

C. 1. ABCD is a rectangle. (Given)
2. ABCD is a parallelogram.(Rectangle→parallelog ram)
3. m∠A=90°, m∠B=90° (Same-side Int. ∠s Thm.)
4. ∠A≅∠B (Rt. ∠s ≅ Thm.)
5. ED¯¯¯¯¯≅EC¯¯¯¯¯ (Def. of mdpt.)(Parallelogram→opp. sides ≅)
6. EA¯¯¯¯¯≅EB¯¯¯¯¯ (Given)
7. △EAD≅ △EBC (SAS Steps 4, 5, 6)

D.1. ABCD is a rectangle. (Given)
2. ABCD is a parallelogram.(Rectangle→parallelog ram)
3. ∠A+∠B=180° (Same-side Int. ∠s Thm.)
4. ∠A≅∠B (Step 3)
5. AD¯¯¯¯¯≅BC¯¯¯¯¯ (Parallelogram→opp. sides ≅)
6. EA¯¯¯¯¯≅EB¯¯¯¯¯ (Given)
7. △EAD≅ △EBC (SAS Steps 4, 5, 6)

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Given ABCD is a rectangle. Which of the following proves △EAD≅△EBC? A. 1. ABCD is a rectangle. (Gi...