Transcript Proving Lines Perpendicular

Proving Lines Perpendicular
Page 4
To prove lines perpendicular:
t
1
Given:
1   2
Prove:
st
Statement
2
s
Reason
1. 1  2
1. Given
2. s  t
2. Two intersecting lines that
form congruent adjacent
angles are perpendicular
Pg. 4 #1
Statement
Reason
1. 1  4
1. Given
2. 2  3
2. Given
3. 1  2  4  3
3. Addition Postulate
4. 1  2  ADC
4  3  BDC
4. Partition Postulate
5. ADC  BDC
5. Substitution Postulate
6. CD  AB
6. Two intersecting lines that
form congruent adjacent
angles are perpendicular
Pg. 4 #2
Statement
12
Reason
1. AC  BC
1. Given
2. CD bisects ACB
2. Given
3. 1  2
3. An angle bisector divides an
angle into two congruent parts
4. CD  CD
4. Reflexive postulate
5. ΔACD  ΔBCD
6. ADC  BDC
5. SAS  SAS
7. CD  AB
7. Two intersecting lines that
form congruent adjacent
angles are perpendicular
6. CPCTC
Pg. 4 #3
Statement
12
4 3
E
Reason
1. PR  PS
1. Given
2. QR  QS
2. Given
3. PQ  PQ
3. Reflexive postulate
4. ΔRPQ  ΔSPQ
5. 1  2
4. SSS  SSS
5. CPCTC
6. PE  PE
7. ΔRPE  ΔSPE
6. Reflexive postulate
8. 3  4
8. CPCTC
9. PQ  RS
9. Two intersecting lines that
form congruent adjacent
angles are perpendicular
7. SAS  SAS