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Advanced Geometry
Section 2.7 Transitive and Substitution Properties
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
A B C D
EF
G
Given FC bisects AFE EB bisects DEF
Prove: AFE ≅ DEF
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Warm Up:
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
AB
C
If A ≅ B, and B ≅ C, then what must be true about A and C?
THEOREM If angles (or segments) are congruent to the same angle (or segment) then the angles (or segments) are congruent. (Transitive Property)
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
THEOREM If angles (or segments) are congruent to congruent angles (or segments) then the angles (or segments) are congruent. (Transitive Property)
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
PROPERTY:Substitution Property: If two things are equal, one can be substituted for the other.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Homework:pg. 97
#3-5, 10, 12,13
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Advanced Geometry
Section 2.8 Vertical Angles
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
DEFINITIONTwo collinear rays that have common endpoints and extend in opposite directions are called OPPOSITE RAYS.
A BC
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
DEFINITIONTwo angles are VERTICAL ANGLES if the rays forming the sides of one and the rays forming the sides of the other are opposite rays.
A
B
CD
EWhich pairs of angles arevertical angles?
What must be true about vertical angle pairs?
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
What must be true about vertical angle pairs?
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
THEOREM If two angles are vertical angles, then they are congruent.
A
B
CD
E
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Assignment
pg. 102# 4, 5, 10, 12, 13
2.Review: 4, 5, 7, 11-18, 20, 21, 32, 33, 35
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
Learner Objective: Students will apply the transitive property of angles and segments, the substitution property, and the Vertical Angle Theorem.
