Given: AC = BD

Prove: AB = CD.

A B C D

2-6 Proving Statements about Segments

Given: AB = CD

Prove: AC = BD.

A B C D

theorem: proven statement

Linear Pair Theorem: If two angles form a linear pair, then they are supplementary.

Proof.

Given: 1 and 2 form a linear pairProve: 1 supp 2

1 2

A B C

D

Statements Reasons

1.

2.

3.

4.

5.

6.

7.

1 and 2 form a linear pair 1.

2.

3.

4.

5.

6.

7. 1 supp 2

given

A B C

D

Congruent Complements Theorem:

Congruent Supplements Theorem:

If two angles are complementary to the same angle (or to two congruent angles) then the two angles are congruent.

If two angles are supplementary to the same angle (or to two congruent angles) then the two angles are congruent.

(Proof): Congruent Complements TheoremIf 2 angles are complementary to the same angle, then they are congruent to each other.

Given:

Prove:

Statements Reasons

(Proof): Congruent Supplements TheoremIf 2 angles are supplementary to the same angle, then they are congruent to each other.

Given:

Prove:

Statements Reasons

1. Given: m 1 = 24, m 3 = 24 1 comp. 2 3 comp. 4

Prove: 2 = 4

Statement Reason

1. __________________ 1. given

2. __________________ 2. given

3. __________________ 3. ____________________

4. 1 = 3 4. ____________________

5. __________________ 5. given

6. __________________ 6. given

7. __________________ 7. _____________________

Right Angle Congruence Theorem: All right angles are congruent.

Statement Reason

1. A and B are right angles 1.

2. m A = 90 ; m B = 90 2.

3. m A = m B 3.

4. 4. Definition of = angles

A

B

Given: A and B are right anglesProve: A B=

3. Given: DAB and ABC are rt. angles ABC = BCD

Prove: DAB = BCD

D

A B

C

Statement Reason

1. _____________________ 1. _____________________

2. _____________________ 2. _____________________

3. _____________________ 3. _____________________

4. ABC = BCD 4. _____________________

5. _____________________ 5. _____________________

4. Given: 1 = 2, 3 = 4 2 = 3

Prove: 1 = 4

B

A C

Statement Reason

1. ______________________ 1. given

2. ______________________ 2. given

3. ______________________ 3. ______________________

4. 3 = 4 4. given

5. ______________________ 5. _______________________

5. Given: m 1 = 63, 1 = 3 3 = 4

Prove: m 4 = 63

Statement Reason

1. ___________________ 1. given

2. ___________________ 2. given

3. ___________________ 3. ____________________

4. ___________________ 4. defn. = angles

5. m 1 = 63 5. given

6. ___________________ 6. ________________________

K

LJ

Statement Reason

1. 1. given

2. 2. given

3. LK = JK 3.

4. LK = JK 4.

5. JK = JL 5.

6. 6.

6. Given: LK = 5, JK = 5, JK = JL

Prove: LK = JL

M

R

X

N

S

Statement Reason

1. 1.

2. 2. Definition of midpoint

3. MX = XN 3.

4. 4. given

5. XN = RX 5.

7. Given: X is the midpoint of MNMX = RX

Prove: XN = RX

R S T

W X Y

Statement Reason

1. 1. given

2. 2. given

3. 3. Segment Addition Postulate

4. XY + WX = RT 4.

5. WX + XY = WY 5.

6. RT = WY 6.

8. Given: RS = XY ST = WX

Prove: RT = WY

Find BC.3x-1 2x+3

A

B C

D9. Given: AB = BC, BC = CD

10.

Given: RT = WY, ST = WX

Prove: RS = XY

Statement Reason1. ____________________ 1. given

2. RT = WY 2. ____________________

3. ____________________ 3. Segment Addition Postulate

4. ____________________ 4. Segment Addition Postulate

5. ____________________ 5. _____________________

6. ST = WX 6. given

7. RS = XY 7.

8. RS = XY 8. ______________________

R S T

W X Y

11. Given: AD = 8, BC = 8, BC = CD

Prove: AD = CD

A D

C

B

Statement Reason

1. ________________ 1. given

2. BC = 8 2. _______________

3. ________________ 3. transitive

4. ________________ 4. Definition of = segments

5. BC = CD 5. ____________________

6. AD = CD 6. _____________________