Question

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Please help with these proofs Part 2

Answer 1

Problem 5

Given:

• CF bisects BD,
• ∠1 ≅ ∠2

To prove CD ≅ BF, we'll first prove the triangles are congruent by AAS as we have one congruent angle pair, there is another pair of vertical angles and congruent sides as part of bisected segment.

Statement Reason

• CF bisects BD Given
• ∠1 ≅ ∠2 Given
• BE = ED Definition of bisector
• ∠3 ≅ ∠4 Vertical angles are congruent
• ΔCED ≅ ΔFEB AAS congruence (adjacent angles and not included side)
• CD ≅ BF CPCTC

• Proved

Problem 6

Given:

• TR bisects SA,
• ST ≅ TA

To prove ∠S ≅ ∠A, we'll first prove the triangles are congruent by SSS as we have one congruent side pair, one more side is common to both triangles, another side pair is congruent as part of bisected segment.

Statement Reason

• TR bisects SA Given
• ST ≅ TA Given
• SR ≅ AR Definition of segment bisector
• TR ≅ TR Reflexive property (common side)
• ΔSTR ≅ ΔATR SSS congruence
• ∠S ≅ ∠A CPCTC

• Proved