Download Students will apply the transitive property of angles and segments

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.
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
Warm Up:
A
B
C
D
Given FC bisects AFE
EB bisects DEF
Prove:
G
F
E
AFE ≅
DEF
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
C
A
B
If
A ≅ B, and
B ≅ C, then what must be
true about A and C?
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
THEOREM
If angles (or segments) are congruent to the same angle (or segment)
then the angles (or segments) are congruent.
(Transitive Property)
THEOREM
If angles (or segments) are congruent to congruent
then the angles (or segments) are congruent.
(Transitive Property)
angles (or segments)
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
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
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
Homework:
pg. 97
#3-5, 10, 12,13
substitution property,
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
and the Vertical Angle Theorem.
substitution property,
DEFINITION
Two collinear rays that have common endpoints and extend in opposite directions are
called OPPOSITE RAYS.
C
A
B
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
DEFINITION
Two angles are VERTICAL ANGLES if the rays forming the sides of one and the rays
forming the sides of the other are opposite rays.
E
A
B
D
What must be true about vertical angle pairs?
C
Which pairs of angles are
vertical angles?
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
What must be true about vertical angle pairs?
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
THEOREM
If two angles are vertical angles,
then they are congruent.
E
A
B
D
C
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
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
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
and the Vertical Angle Theorem.
substitution property,
Learner Objective: Students will apply the transitive property of angles and segments, the
the Vertical Angle Theorem.
substitution property, and
Learner Objective: Students will apply the transitive property of angles and segments, the
the Vertical Angle Theorem.
substitution property, and
Learner Objective: Students will apply the transitive property of angles and segments, the
the Vertical Angle Theorem.
substitution property, and
Learner Objective: Students will apply the transitive property of angles and segments, the
the Vertical Angle Theorem.
substitution property, and
Learner Objective: Students will apply the transitive property of angles and segments, the
the Vertical Angle Theorem.
substitution property, and