2-6 Proving Statements about Segments
Given: AC = BD
Prove: AB = CD.
A
B
C
D
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:
Prove:
D
A
1 and 2 form a linear pair
1 supp 2
Statements
1.
1 and
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
1 supp
B
Reasons
2 form a linear pair
2
7.
2
1
given
C
A
B
D
C
Congruent Complements Theorem:
If two angles are complementary to the same angle
(or to two congruent angles) then the two angles are
congruent.
Congruent Supplements Theorem:
If two angles are supplementary to the same angle
(or to two congruent angles) then the two angles are
congruent.
(Proof): Congruent Complements Theorem
If 2 angles are complementary to the same angle, then
they are congruent to each other.
Given:
Prove:
Statements
Reasons
(Proof): Congruent Supplements Theorem
If 2 angles are supplementary to the same angle, then
they are congruent to each other.
Given:
Prove:
Statements
Reasons