Question

Given: C is the midpoint of BD.

Prove: ΔACB ≅ ΔACD

Triangle A B D is shown. A line is drawn down from point A to point C to form a right angle. Triangle A C B and A C D are formed by the line.
Complete the two-column proof.

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Answer 1

Statement | Reason
---|---
1. C is the midpoint of BD. | 1. Given
2. BC = CD. | 2. Definition of midpoint
3. AC ⟂ BD. | 3. Given (AC is drawn perpendicular to BD)
4. ∠ACB and ∠ACD are right angles. | 4. Definition of perpendicular lines
5. ∠ACB = ∠ACD. | 5. All right angles are congruent
6. AC = AC. | 6. Reflexive property of equality
7. ΔACB ≅ ΔACD. | 7. SAS (BC = CD, AC = AC, included ∠ACB = ∠ACD)

Therefore ΔACB ≅ ΔACD.