Question

Need help!!!
complete these proofs.

Answer 1

Explanation:

23.

1. Alternate exterior angles

2. Vertical Angles

3. Vertical Angles

4. Alternate Interior angles

24.

1. Given

2. Definition of an Angle Bisector

3. Reflexive Property

4. ASA (Angle side angle)

Answer 2

23.

1. Given
2. Being Vertically Opposite angle
3. Being Vertically Opposite angle
4. From statement 1, 2 and 3

24.

1. Given
2. Definition of angle bisector
3. Reflexive Property or being same side
4. By Angle-Angle-SIde or AAS axiom

Explanation:

For proof 23.

Given:

∡1 ≅ ∡4

To Prove:

∡2 ≅ ∡3

Proof:

Statement ( Reason in bracket)

1. ∡1 ≅ ∡4 (Given)

2. ∡2 ≅∡ 1 (Being Vertically Opposite angle)

3. ∡3 ≅ ∡4 (Being Vertically Opposite angle)

4. ∴∡2 ≅ ∡3 (From statement 1, 2 and 3)

`\hrulefill`

For proof 24.

Given:

BD bisects ∡ABC and ∡ADC

To Prove:

ΔABD ≅ ΔCBD

Proof:

Statement (Reason in bracket)

1. BD bisects ∡ABC and ∡ADC (Given) Angle

2. ∡ABD ≅ ∡CBD; ∡ADB ≅ ∡CDB. (Definition of angle bisector) Angle

3. BD ≅ BD (Reflexive Property or being same side) Side

4. ∴ΔABD ≅ ΔCBD (By Angle-Angle-SIde or AAS axiom )

`\textsf{Hope this Helps: }`