Transcript Geometry 2.6 / 2.7

SWLT: Write proofs using geometric theorems and use
properties of special pairs of angles.
 In a proof, you make one
statement at a time, until
you reach your conclusion.
 Because the Statements
made are based on facts,
you are using deductive
reasoning.
 Usually the 1st statementand-reason pair written is
the given information
Statements
Reasons
M
A
Reasons
Statements
1.
2.
3.
4.
5.
6.
M is a Midpoint of AB
AM ≅ MB
AM = MB
AM + MB = AB
AM + AM = AB
2  AM = AB
B
1.
2.
3.
4.
5.
6.
Given
Definition of Midpoint
Def. of Congruent
Segments
Segment Add. Postulate
Substitution Prop. Of Eq.
Distributive Prop. Of Eq.
(Draw two Separate Segments)
B
A
Reasons
Statements
1.
2.
3.
4.
5.
B is a Midpoint of AC.
C is a Midpoint of BD
AB ≅ BC
BC ≅ CD
AB ≅ CD
AB = CD
C
1.
2.
3.
4.
5.
Given
Definition of Midpoint
Definition of Midpoint
Transitive Property
Def. of Congruence
D
 Congruent Complements Theorem
 Congruent Supplements Theorem
 If two angles are complementary to
 If two angles are supplementary to
the same angle, then they are
congruent
 If m1 + m2 = 90° and
m2 + m3 = 90°, then 1 ≅ 3
the same angle, then they are
congruent
 If m4 + m5 = 180° and
m5 + m6 = 180°, then 4 ≅ 6
5
3
2
1
4
6
(Congruence of Supplements Proof)
2
1
Reasons
Statements
1.
2.
3.
4.
5.
6.
1 & 2 are supplements,
3 & 2 are supplements.
m1 + m2 = 180°
m3 + m2 = 180°
m1 + m2 = m3 + m2
m1 = m3
m1 ≅ m3
3
1.
2.
3.
4.
5.
6.
Given
Def. of Supplementary
Angles
Def. of Supplementary
Angles
Transitive Property
Subtraction Property
Def. of Congruence