Question

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Please help me with these proofs Part 4

Answer 1

Problem 3

Given:

• RC ⊥ OK,
• RK ≅ KS

The triangles ΔKRO and ΔKCO are right triangles with common leg and congruent hypotenuse. It is sufficient for HL (Hypotenuse - leg) congruence. RK and KC are hypotenuse and OK is common leg.

Statement Reason

• RC ⊥ OK Given
• RK ≅ KS Given
• ∠1 and ∠2 are right angles Definition of perpendicular
• OK ≅ OK Reflexive property (common side)
• ΔKRO ≅ ΔKCO HL congruence

• Proved

Problem 4

Given:

• LG bisects ∠GFA,
• ∠F ≅ ∠A

To prove FG ≅ AG, we'll first prove the triangles are congruent by AAS as we have one congruent angle pair, one side is common to both triangles, another pair of congruent angles is formed by the angle bisector. The common side is adjacent to one of the congruent angles but not included.

Statement Reason

• LG bisects ∠GFA Given
• ∠F ≅ ∠A Given
• ∠1 ≅ ∠2 Definition of angle bisector
• LG ≅ LG Reflexive property (common side)
• ΔLGA ≅ ΔLGF AAS congruence
• FG ≅ AG CPCTC

• Proved