parallel lines properties of angles formed by parallel lines and a transversal

Parallel Lines

Properties of Angles Formed by Parallel Lines and a Transversal

Parallel lines (Definition)

Symbol:

A line that intersects both parallel lines is called a transversal. Which is the transversal in the diagram above?

Parallel lines

and line t is the transversal

Corresponding Angles

Angles in the same position1 and 52 and 63 and 74 and 8

Alternate Angles (they alternate…)

Alternate Interior: inside the parallel lines, on either side of the transversal

Alternate Exterior: outside the parallel lines, on either side of the transversal

Same Side Interior These angles are on the same side of the transversal and inside the parallel lines.

Investigation

1) Use the ruler to draw a pair of parallel lines, intersected by a transversal. Label the angles.

2) Place a piece of patty paper over angles 1,2,3 and 4. Copy them onto the patty paper.

3) Slide the patty paper down to compare angles 1-4 with angles 5-8

4) Measure angle 1. Use this measure to calculate the measure of the other 7 angles.

Links to Geogebra Given one angle, Find others-80178.ggb

All angles-143981.ggb

TheoremsIf two parallel lines are intersected by a transversal then:

Corresponding Angles are equalAlternate Interior Angles are equal Alternate Exterior Angles are equal Same Side Interior Angles are supplementary

I Do: Find the measure of each angle. Justify.

We Do: Find the measure of each angle. Justify.

Your turn: Find the measure of each angle. Justify.

We Do: Find the value of x.

Your Turn: Find the value of x.

Geometry in nature…

Geometry around us…

Exit Slip

What did we do today?What did you learn? What part of the lesson helped you learn it better?What are you still confused about?