Geometry
Essentials, Day 4
Today:


Name ____________________________
You will learn how to use deductive reasoning to write a two-column proof.
At the end of class you will be able to prove statements about segments, angles, and angle pair relationships.
You will be able to write a two-column proof to justify your steps in solving an algebraic equation.
Postulates:
Theorems:
Proofs:
Points/Lines/Planes Postulates
Postulate
1)
2)
3)
4)
5)
6)
Illustration
Perpendiculars
Def.
Perpendicular
lines
planes
line and a plane
2𝑥 + 5 = 30 − 3𝑥
5𝑥 + 5 = 30
5𝑥 = 25
𝑥=5
c.
d. 𝟑 + 𝟐(𝟓𝒙 + 𝟏) = 𝟔𝟑
Statements
Reasons
𝑚∠1 = 𝑚∠3
𝑚∠1 + 𝑚∠2 = 𝑚∠2 + 𝑚∠3
𝑚∠1 + 𝑚∠2 = 𝑚∠𝐷𝐵𝐶
𝑚∠2 + 𝑚∠3 = 𝑚∠𝐸𝐵𝐴
𝑚∠𝐷𝐵𝐶 = 𝑚∠𝐸𝐵𝐴
Definition of Congruent Angles – If the measures of two angles are congruent then the angles are
congruent
𝑚∠1 = 𝑚∠3