Math 2 7.6Proving Lines parallel

• Last time we said that if two lines are parallel and they are cut by a transversal then...

• Certain angles are congruent• Certain angles are supp.• So on and so forth.

• Today we will go the other way• We will say that IF a transversal

cuts two lines• And IF result certain angles are

congruent And IF certain angles are supplementary

Then the lines must be parallel

Conditional Statements• AKA if-then statements

• If a number is divisible by 2 then it is an even number

Conditional Statements• The part following the if is the

HYPOTHESIS• The part following the then is the

CONCLUSION

• Hypothesis:–A number is divisible by 2

• Conclusion:–It is an even number

So…From the 1st example

• If it is raining outside, then the sidewalks are wet.

• If a player misses practice, then he cannot start in the game.

Identify the H and the C

Some are True and Some are False

• If I am in Math class then I am happy to be at school.

• If someone has short hair then they are a boy.

They are not always explicit

• All dogs have fleas.• I can go to the park after I clean my

room.• My mom gives me $10 for every A on

my report card.

• Try to express the following statements in IF – THEN form.

WRITING THE CONVERSE

It is easy…Really

• The converse of a conditional statement is made by exchanging the hypothesis and the conclusion.

Look how easy

• If a figure is a triangle, then it has three angles.

If a figure has three angles then it is a Triangle.

Let’s try again

• Just swap the Hypothesis and the Conclusion…Ready?

• If you play a musical instrument, then you will do well in school.

• If you do well in school, then you will play a musical instrument.

Its called the Converse

• Think of Shoes! • Swap the left shoe with the right

shoe!!!• Swap the IF “shoe” with

the THEN “shoe”

• If it is raining outside, then the sidewalks are wet.

• If the sidewalks are wet, then it is raining outside.

• If you are a couple, then you go to Prom.

• If you go to prom, then you are a couple.

Last homework we said• If lines are parallel, then

Alt Int Angles are Congruent.

Todays homework deals with the converse

IF Alt Int Angles are Congruent Then the Lines are Parallel.

Find x so that a ii b

a

b

x

11070

Find x so that a ii b

a

b

4x

80

Find x so that a ii b

a

b3x + 5

50

Find x so that a ii b

a

b

2x-4

Find x so that a ii b

a

b

10x-86x+12