Download lesson 3.2 Geometry.notebook

lesson 3.2 Geometry.notebook
Warm Up
Identify each angle pair.
1. ∠1 and ∠3
2. ∠3 and ∠6
3. ∠4 and ∠5
4. ∠6 and ∠7
5. ∠1 and ∠5
6. ∠1 and ∠6
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
E
Parallel segments?
D
F
G
Perpendicular segments?
H
C
Skew segments?
A
B
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
Let's Remember...
Linear Pair Theorem states: If two angles form a linear pair, then they are supplementary.
____________________________________
Vertical Angles Theorem states:
Vertical angles are congruent.
____________________________________
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
GOAL
Prove and use theorems about the angles formed by parallel lines and a transversal.
Postulate ~ 1 total • Corresponding Angles Postulate
Theorems ~ 3 total • Alternate Interior Angles Theorem
• Alternate Exterior Angles Theorem
• Same­Side Interior Angles Theorem
2 1
1 2
2
1
1
2
lesson 3.2 Geometry.notebook
October 29, 2015
1) Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of congruent
corresponding angles are __________.
lesson 3.2 Geometry.notebook
October 29, 2015
Example 1: Using the Corresponding Angles Postulate
Find each angle measure.
A. m∠ECF
B. m∠DCE
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Your Turn! #1
Find m∠QRS.
(5x + 2)o
(6x ­ 24)o
lesson 3.2 Geometry.notebook
October 29, 2015
Complete this conjecture:
If a transversal is perpendicular to two parallel lines, then
all eight angles formed are congruent
______________________________________________
lesson 3.2 Geometry.notebook
October 29, 2015
Remember that postulates are statements that are accepted without proof.
Since the Corresponding Angles Postulate is given as a postulate, it can be used to prove the next three theorems.
lesson 3.2 Geometry.notebook
October 29, 2015
2) Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, the the pairs of congruent
alternate interior angles are ____________.
How could we prove this Theorem using what we have learned so far?
statements
reasons
lesson 3.2 Geometry.notebook
October 29, 2015
3) Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the two congruent
pairs of alternate exterior angles are ______________.
4) Same­Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then the two supplementary
pairs of same­side interior angles are ______________.
lesson 3.2 Geometry.notebook
Let's sum it up...
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Example 2: Finding Angle Measures
Find each angle measure.
A. m∠EDG
B. m∠BDG
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Your Turn! #2
Find m∠ABD.
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Example 3: A little tougher
Find x and y in the diagram.
Which two given angles are Alternate Interior Angles?
By the Alternate Interior Angles
Theorem, (5x + 4y)° = 55°.
Which two given angles are corresponding angles?
By the Corresponding Angles Postulate, (5x + 5y)° = 60°.
Systems of Equations (Remember Algebra??)
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Your Turn! #3
Solve for x and y.
An acute angle will be 180° – 125°, or 55°. The other acute angle will be 180° – 120°, or 60°. lesson 3.2 Geometry.notebook
October 29, 2015
Finding these angles in other figures
lesson 3.2 Geometry.notebook
October 29, 2015
3.2 Angles Formed by Parallel Lines and Transversals
Class Work
State the theorem or postulate that is related to the measures of the angles in each pair. Solve for x.
1. m∠1 = 120°, m∠2 = (60x)°
2. m∠2 = (75x – 30)°, m∠3 = (30x + 60)°
3. m∠3 = (50x + 20)°, m∠4= (100x – 80)°
4. m∠3 = (45x + 30)°, m∠5 = (25x + 10)°
lesson 3.2 Geometry.notebook
October 29, 2015
lesson 3.2 Geometry.notebook
October 29, 2015
Homework: 2nd/6th: Due Friday
3.2 pg 159 #13­23, 25, 27, 28, 39
Class Work due Today: pg 158 #1­12
lesson 3.2 Geometry.notebook
October 29, 2015