Question

1) AB¯≅AD¯ Given

2)∠ACD is a right angle.- Given
3) m∠ACD=90° -Definition of right angle
4) m∠ACB=90° -Given
5) m∠ACB=m∠ACD -Transitive Property of Equality
6) ∠ACB≅∠ACD Definition of congruent angles
7) C is the midpoint of BD¯ Given
8)C bisects BD¯ ?
9) BC¯≅CD¯ Definition of bisect
10) AC¯≅AC¯ Reflexive Property of Congruence
11) △ABC≅△ADC -SAS Congruence Postulate


What is the correct reason for Statement 8?

Given


Definition of bisect


Definition of congruent segments


Definition of midpoint

Answer 1

the answer is the definition of midpoint

Answer 2

By definition of midpoint.

Explanation:

proof:

1.Statement:
`\overline{AB}\cong \overline{AD}`.

Reason: Given.

2.Statement:
`\angleACD` is a right angle.

Reason:Given.

3.Statement:
`m\angle ACD=90^(\circ)`.

Reason: By definition of right angle.

4.Statement:
`m\angle ACB=90^(\circ)`.

Reason: Given.

5.Statement:
`m\angle ACB=m\angle ACD`

Reason: Transitive property of equality.

6. Statement:
`m\angle ACB\cong m\angle ACD`.

Reason: By definition of congruent triangles.

7.C is the midpoint of
`\overline {BD}`.

Reason: Given.

8.Statement: C bisect
`\overline{BD}`

Reason: By definition of midpoint.

9.Statement:
`\overline{BC}\cong \overline{CD}`

Reason: By definition of bisect.

10.Statement:
`\overline{AC}\cong\overline{AC}`

Reason: By reflexive property of congruence.

11.Statement:
`\triangle ABC\cong \triangle ADC`.

Reason: SAS congruence postulate.