Geometry 3.3

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# Geometry 3.3 - PowerPoint PPT Presentation

Geometry 3.3 . Proving Lines Parallel. Learning Target. Students should be able to… Use the angles formed by a transversal to prove two lines are parallel. Warm-up. Homework Check. Homework Check. Homework Check. Homework Check. Homework Check. Homework Check.

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## PowerPoint Slideshow about 'Geometry 3.3' - arnold

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### Geometry 3.3

Proving Lines Parallel

Learning Target
• Students should be able to…
• Use the angles formed by a transversal to prove two lines are parallel.
Review…What is a converse?

A converse is found by switching the hypothesis and the conclusion.

Switch the “if” and the “then” statement.

The converse does not have to be true.

Practicing Converse Statements

Original Statement:

If my dog is a Dalmatian, then it has spots.

Converse Statement:

If my dog has spots, then it is a Dalmatian.

Is the converse true???

Practicing Converse Statements

Original Statement:

If it is sunny outside, then it won’t rain.

Converse Statement:

If it won’t rain, then it will be sunny outside.

Is the converse true???

Practicing Converse Statements

Original Statement:

If my cell phone is turned off, then it will not ring.

Converse Statement:

If my cell phone will not ring, then it is turned off.

Is the converse true???

Practicing Converse Statements

Do you have a statement to try?

Original Statement:

Converse Statement:

Is the converse true???

Connecting

Today we are using the converse with the theorems or postulates we discovered yesterday in section 3-2.

Who can remember what any of the theorems or postulates were yesterday?

Corresponding Angles Postulate

Corresponding Angles Postulate:

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Converse of the Corresponding Angles Postulate:

If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.

Alternate Interior Angles Theorem

Alternate Interior Angles Postulate:

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Converse of the Corresponding Angles Postulate:

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

Alternate Exterior Angles Theorem

Alternate Exterior Angles Postulate:

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Converse of the Corresponding Angles Postulate:

If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

Same-Side Interior Angles Theorem

Alternate Exterior Angles Postulate:

If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary.

Converse of the Corresponding Angles Postulate:

If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.

Corresponding Angles Postulate

If two parallel lines are cut by a transversal their corresponding angles are congruent.

Now we are going to look at the converse of this postulate.

Converse of the Corresponding Angle Postulate:

If corresponding angles are congruent, then the two lines are parallel.

3-3 Guided Notes

Converse of the Alternate Exterior Angle Theorem

Converse of the Same-Side Interior Angle Theorem

Converse of the Alternate Interior Angle Theorem

Homework Assignment
• We will be having a Review/Quiz day on Monday.
• It will cover 3.1 – 3.3. We will work through practice problems in class before taking the quiz.
• Homework Assignment:
• Page 166 – 167 #1 – 9 odd