Converses Converse Switching the hypothesis and conclusion of a conditional statement For our proofs last class what was always our given What were we trying to prove Now we want to prove the opposite so what will we need to be given What will we be trying to prove ID: 734249
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Slide1
Warm Up
Section Name: Proofs with Transversals 2Slide2
Converses
Converse: Switching the hypothesis and conclusion of a
conditional statement
.
For our proofs last class what was always our given? What were we trying to prove?
Now we want to prove the opposite so what will we need to be given? What will we be trying to prove? Slide3
Converses
Converse: Switching the hypothesis and conclusion of a
conditional statement
.
Corresponding Angles Postulate:
If two lines are parallel, then their corresponding angles are congruent.
Converse of the Corresponding Angles Postulate :
Consecutive Interior Angles Theorem:
Given two lines are parallel, then their consecutive interior angles are supplementary.
Converse of the Consecutive Interior Angles Theorem:Slide4
Application
Which of the following statements will justify that
, explain.
a.
and
are supplementary.
b.
and
are congruent.
c.
d. and are congruent. e. and are congruent.
Slide5
Matching Activity
You will each be given a set of four diagrams. Each of the different diagrams are labelled A, B, C, or D.
I will put a statement on the board. You will decide which diagram matches the statement. You will then write the letter for that diagram on your whiteboard and hold it up for me to check.
Once everyone has answered we will discuss the answer(s) as a class.Slide6
Every diagram tells its own story…
by the converse of the alternate interior angles theorem.
Slide7
Every diagram tells its own story…
is supplementary to
by the consecutive interior angles theorem.
Slide8
Every diagram tells its own story…
by the corresponding angles theorem.
Slide9
Every diagram tells its own story…
by the alternate interior angles theorem.
Slide10
Every diagram tells its own story…
by the converse of the alternate exterior angles theorem.
Slide11
Every diagram tells its own story…
by the alternate exterior angles theorem.
Slide12
Every diagram tells its own story…
by the converse of the corresponding angles theorem.
Slide13
Every diagram tells its own story…
by the converse of the consecutive interior angles theorem.
Slide14Slide15
Warm-up
Section Name: Unit 3 Review
Solve for all missing angle measures.
Given:
Slide16Slide17
Complete the following proofs:
Warm-Up
Given:
Prove:
Given:
Prove:
Review Day NotesSlide18Slide19
Solve for all missing angle measures.
107°
Warm-UpSlide20
What is enough information to prove that lines are perpendicular?
What is enough information to prove that lines are parallel?
Slide21
Practicing the transitive property.
Slide22Slide23
Warm-Up
T
S
R
2
1
4
3
5
6
78Name all the different angle relationships. Give an example. State whether they are congruent or supplementary. Test Today Slide24
Given
and the measure of
Find the measure of ALL other angles.