Download lesson 3.3 Geometry.notebook

lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
Warm Up
Find the measure of each angle and state the theorem or postulate you used.
1. mÐ1
2. mÐ2
1
2
3. mÐ3
4. mÐ4
5. mÐ5
6. mÐ6
7. mÐ7
4 7
5 6
35o
3
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
3­3 Proving Lines Parallel
GOAL
Use the angles formed by a transversal to prove two lines are parallel.
Today we are doing the converse of last class!
lesson 3.3 Geometry.notebook
November 03, 2015
For all theorems/postulates presented last class,
what was the hypothesis? then ....angles the conclusion?
If 2 lines are parallel
lesson 3.3 Geometry.notebook
November 03, 2015
3­3 Proving Lines Parallel
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Is the converse of a definition true? Share with a partner and use the definition of parallel lines to prove or disprove your point.
Parallel lines are coplanar and do not intersect.
"If two lines are coplanar and do not intersect, then they are parallel"
lesson 3.3 Geometry.notebook
November 03, 2015
last class...
If two parallel lines are cut by a transversal, then all pairs of corresponding angles are congruent
Today... If one pair of corresponding angles are congruent,
then the two lines are parallel
lesson 3.3 Geometry.notebook
November 03, 2015
Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m∠3 = (4x – 80)°, m∠7 = (3x – 50)°, x = 30
Statements
Reasons
m∠3 = 4(30) – 80 = 40
Substitute 30 for x.
m∠8 = 3(30) – 50 = 40
Substitute 30 for x.
m∠3 = m∠8
∠3 ≅ ∠8
ℓ || m Trans. Prop. of Equality
Def. of ≅ ∠s.
Conv. of Corr. ∠s Post.
lesson 3.3 Geometry.notebook
November 03, 2015
Your Turn! #1
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m∠7 = (4x + 25)°, m∠5 = (5x + 12)°, x = 13
lesson 3.3 Geometry.notebook
3­3 Proving Lines Parallel
More converses from last class...
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
∠4 ≅ ∠8
lesson 3.3 Geometry.notebook
November 03, 2015
3­3 Proving Lines Parallel
Your Turn #2
Name the postulate or theorem that proves p || r.
1. ∠4 ≅ ∠5
2. ∠2 ≅ ∠7
3. ∠3 ≅ ∠7
4. ∠3 and ∠5 are supplementary.
lesson 3.3 Geometry.notebook
November 03, 2015
Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
m∠2 = (10x + 8)°, m∠3 = (25x – 3)°, x = 5
lesson 3.3 Geometry.notebook
November 03, 2015
Your Turn! #3
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
m∠3 = 2x°, m∠7 = (x + 50)°, x = 50
lesson 3.3 Geometry.notebook
November 03, 2015
How we will use this moving forward....
Prove that the quadrilateral is a parallelogram (opposite sides are parallel)
60o
120o
60o
120o
lesson 3.3 Geometry.notebook
November 03, 2015
Example 4: Proving Lines Parallel
m
ℓ
Given: p || r , ∠1 ≅ ∠3
p
1
2
Prove: ℓ || m
r
3
lesson 3.3 Geometry.notebook
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
Proof Pair Work
• There are 12 proofs on the paper. Complete 9 of them. • #6, #11 and #12 are bonus proofs (E.C.)
• Come to me when you have completed a proof to check your answer.
• One of these proofs will be on your chapter test.
lesson 3.3 Geometry.notebook
Homework: Due Monday 3.3 pg 166 #1­10, 22, 24­35
November 03, 2015
lesson 3.3 Geometry.notebook
3­3 Proving Lines Parallel
Your Turn #3
Given: ∠1 ≅ ∠4, ∠3 and ∠4 are supplementary.
Prove: ℓ || m
November 03, 2015
lesson 3.3 Geometry.notebook
November 03, 2015
Proving Lines are Parallel ~ How could I make sure line p is parallel to line t
p
t
lesson 3.3 Geometry.notebook
November 03, 2015