Question

PLEASE HELP
complete these proofs.

Answer 1

3. Definition of a right triangle

4. Reflexive property

5.
`\triangle BDF \cong \triangle BEF` (HL)

6. CPCTC

7. Definition of an angle bisector

Answer 2

3. From statement 2 or Definition of right-angled triangle

4. Reflexive property

5. RHS axiom

6. Being congruent angle or Property of congruent triangle

7. From statement 6 and property of bisector

Explanation:

Given:

DF ≅ EF, DF ⊥ AB; EF ⊥BC.

Prove:
BF bisects ∡ABC

Statements( Reason in bracket)

1. DF ≅ EF, DF ⊥ AB; EF ⊥BC (Given)

2. ∡BDF and ∡BEF are rt. ∡s (Definition of ⊥ lines)

3. ΔBDF and ΔBEFare rt. Δs. (From statement 2 or Definition of right angled triangle)

4. BF ≅ BF. (Reflexive property)

5. ∴ ΔBDF ≅ ΔBEF (RHS axiom)

6. ∡DBF ≅ ∡EBF. (Being congruent side of congruent triangle or Property of congruent triangle)

7. ∴ BF bisects ∡ABC (From statement 6 and property of bisector)

`\textsf{Hope This Helps. Good Luck!!!}`