Question

What is the missing statement in the proof? Scroll down to see the entire proof.

Answer 1

Answer: C. $\angle BCA\cong \angle DCB$ is the missing statement.

Explanation: Given: ΔABC with m∠ABC = 90° (view diagram)

Prove: $AB^2 + BC^2 = AC^2$

Proof:  1. Draw $BD\perp AC$ (construction)

 2. $\angle ABC\cong\angle BDC$  (Angles with the same measure are congruent.)

3. $\angle BCA\cong \angle DCB$ (Reflexive Property of Congruence)

4. $\triangle ABC\sim \triangle BDC$  (AA criterion for similarity)

5. BC:DC=AC:BC  (Corresponding sides of similar triangles are proportional.)

 6.$BC^2= AC\times DC$  (cross multiplication)----------(1)

7. $\angle ABC\cong \angle ADB$ (Angles with the same measure are congruent)

8. $\angle BAC\cong \angle DAB$ (Reflexive Property of Congruence)

9. $\triangle ABC\sim \triangle ADB$  (AA criterion for similarity)

10.  AB:AD=AC:AB⇒$AB^2=AC.AD$ --------------(2)

equation (1) + equation (2) ⇒$AB^2+BC^2= AC(DC+AD)$⇒$AB^2+BC^2= AC^2$

Answer 2

B is the correct answer