Download September 06, 2013

September 06, 2013
Geometry
Unit A: Basics of Geometry
Notes Day 7
Objectives:
*Identify types of angles including linear pair, supplements, complements, vertical,
adjacent to prove and apply theorems about angles
*Understand and use the definition of transversal and identify types of angles
including alternate interior, alternate exterior, same-side interior, same-side exterior
and corresponding to prove and apply theorems about angles
*Prove and use properties of parallel lines cut by a transversal
Assignment: Worksheet 7
Remember this Vocabulary?
Vertical Angles
Adjacent Angles
Complementary Angles
Supplementary Angles
Ex 1 Identifying Angle Pairs
In the diagram identify pairs of numbered angles that are related in the following ways:
1. Complementary
2. Supplementary
3. Vertical
4. Adjacent
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What can you conclude from a drawing? What can you NOT conclude from a drawing?
Ex 2 Making Conclusions From a Diagram
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Useful Theorem:
Vertical Angles Theorem-Vertical angles are congruent
Ex 3 Practice with proofs and plans.
Prove Alternate Interior Angles Theorem
Ex 4 Prove Same-Side Interior Angles Theorem
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15
14
5
0°
12
77
11
4
10
9
3
7
6
2
5
4
1
2
0
49°
0
1
3
8
13
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15
14
13
5
12
11
237
4
10
9
8
3
7
6
2
5
4
3
1
2
1
90°
0
0
0°
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Ex 5 Practice with Proofs and Plans
More Useful Theorems:
Congruent Supplements Theorem-If two angles are supplements of the same angle (or
of congruent angles), then the two angles are congruent.
Congruent Complements Theorem- If two angles are complements of the same angle
(or of congruent angles), then the two angles are congruent.
Right Angles Theorem-All right angles are congruent.
Theorem-If two angles are congruent and supplementary, then each is a right angle.
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Ex 6 Comparing Types of Proofs
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Ex 7 Practicing Proofs-Prove the Congruent Complements Theorem
Even More Useful Theorems:
Theorem-If two lines intersect to form a linear pair of congruent angles, then the lines are
perpendicular.
Theorem-If two sides of two adjacent acute angles are perpendicular, th
en the angles are
complementary.
Theorem-If two lines are perpendicular, then they intersect to form four right angles.
Theorem- If two lines are parallel to the same line, then they are parallel to each other.
Theorem- In a plane, if two lines are perpendicular to the same line, then they are parallel
to each other.
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Ex 8 Practicing Proofs…One more flow
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0° 211
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113
0°
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