advanced geometry section 2.7 transitive and substitution properties learner objective: students...

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.