Download 3.3 I can apply postulates and algebraic proofs to prove statements

3.3 I can apply postulates and algebraic proofs to prove statements.
NAME___________________________
Geometry Proofs
Match the situation with the likely reasoning/postulate.
1. M is the midpoint of AB, so AM = MB.
2. HG is the angle bisector of ∠ XHZ, so ∠ XHG = ∠ GHZ.
3. Two segments need to be totaled together.
4. Two angles need to be totaled together.
5. One segment has the same measure as another segment.
6. One angle has the same measure as another angle.
A. Angle Addition Postulate
B. Definition of Congruent Segments
C. Definition of Midpoint
D. Segment Addition Postulate
E. Definition of Angle Bisector
F. Definition of Congruent Angles
MARK THE DIAGRAM WITH THE GIVEN INFORMATION. Then, fill in the blanks to complete the proofs.
7.
Given
LS = LS
AL + LS = SK + LS
AL + LS = AS
Segment Addition Postulate
Segment Addition Postulate
AS = LK
Substitution Property
8.
̅̅̅̅ ⊥ 𝐵𝐷
̅̅̅̅
𝐴𝐵
∠
is a right angle
𝑚∠𝐴𝐵𝐷 = ______
Def. of Perpendicular Lines
Def. of a Right Angle
𝑚∠𝐴𝐵𝐷 = 𝑚∠1 + 𝑚∠2
𝑚∠1 + 𝑚∠2 = 90°
Given
𝑚∠1 + 𝑚∠3 = 90°
9.
10.
11.
Def. of Angle Bisector
∠𝐴𝐵𝐷 + ∠𝐷𝐵𝐶 = ___________
∠𝐴𝐵𝐷 + ∠________ = ∠_________
Substitution Property
2 ⋅ ∠________ = ∠𝐴𝐵𝐶
Combining Like Terms
Division Property of Eq.