SOLUTION: TWO PROOFS FOR THE SAME PICTURE. Please explain.
1. Given: BD bisects AC, AB ≅ BC.
Prove: angle C ≅ angle A
2. Given: BD is perpendicular to AC, AB ≅ BC.
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-> SOLUTION: TWO PROOFS FOR THE SAME PICTURE. Please explain.
1. Given: BD bisects AC, AB ≅ BC.
Prove: angle C ≅ angle A
2. Given: BD is perpendicular to AC, AB ≅ BC.
P
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Question 732383: TWO PROOFS FOR THE SAME PICTURE. Please explain.
1. Given: BD bisects AC, AB ≅ BC.
Prove: angle C ≅ angle A
2. Given: BD is perpendicular to AC, AB ≅ BC.
Prove: angle CBD ≅ angle ABD
Answer by MathLover1(20849) (Show Source):
1.BD bisects AC, AB ≅ BC........given
2.AD ≅CD.........................def. of bisector
3.BD ≅BD.........................reflexive property
4. triangle ADB ≅BDC.............SSS
5.angle C ≅ angle A......CPCTC
2. Given: BD is perpendicular to AC, AB ≅ BC.
Prove: angle CBD ≅ angle ABD
1.BD is perpendicular to AC, AB ≅ BC.......given
2.angles ABD =angle BDC=90 ..............BD is perpendicular to AC
3. BD = BD............................ common
4. triangles ABD and CBD are ͭ............ ASA
5. angle CBD ≅ angle ABD ..........RHS congruency
