Properties of Parallel Lines

NAME ______PD____ DATE______INVESTIGATION: PROPERTIES OF PARALLEL LINES

STEP 1: Go to the following website: http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php

STEP 2: Click on the DIRECTIONS button located under the “Angles of Parallel Lines and A Transversal” heading.

STEP 3: Carefully READ the directions for how to move the lines, then click the DIRECTIONS button again to close the box.

STEP 4: Experiment with moving the parallel lines and the transversal. Roll the mouse over different angles and observe how the measurements light up.

PART 1: CORRESPONDING ANGLES Click on the button labeled CORRESPONDING ANGLES located on the right hand side of the page. Corresponding angles will be color-coded.

A. Locate 2 pairs of corresponding angles and record their measurements: ANGLE MEASUREMENT 1a.

Sketch the BOTH Corresponding Angles below. Accurately, label the angles WITH the appropriate degrees NAME ______PD____ DATE______

B. MOVE the parallel lines and the transversal. Locate 2 pairs of corresponding angles and record their measurements: ANGLE MEASUREMENT 3a.

Sketch TWO MORE Corresponding Angles with their correct labels and degrees

What do you notice about the corresponding angles?

Compare your results with your partner(s). Make a conjecture based on the information you collected.

When parallel lines are cut by a transversal, corresponding angles formed are______. (CORRESPONDING ANGLES CONJECTURE) NAME ______PD____ DATE______PART 2: ALTERNATE INTERIOR ANGLES Click on the button labeled ALTERNATE INTERIOR ANGLES located on the right hand side of the page. Alternate interior angles will be color-coded.

A. Locate 2 pairs of alternate interior angles and record their measurements: ANGLE MEASUREMENT 1a.

Sketch a TWO pairs of Alternate Interior Angles below. Accurately, label the angles WITH the appropriate degrees NAME ______PD____ DATE______

B. MOVE the parallel lines and the transversal. Locate 2 pairs of alternate interior angles and record their measurements: ANGLE MEASUREMENT 3a.

Sketch TWO more pairs of Alternate Interior Angles below. Accurately, label the angles WITH the appropriate degrees

What do you notice about the alternate interior angles?

When parallel lines are cut by a transversal, alternate interior angles formed are______. (ALTERNATE INTERIOR ANGLES CONJECTURE) NAME ______PD____ DATE______PART 3: ALTERNATE EXTERIOR ANGLES Click on the button labeled ALTERNATE EXTERIOR ANGLES located on the right hand side of the page. Alternate exterior angles will be color-coded.

A. Locate 2 pairs of alternate exterior angles and record their measurements: ANGLE MEASUREMENT 1a.

Sketch TWO pairs of Alternate EXTERIOR Angles below. Accurately, label the angles WITH the appropriate degrees

B. NAME ______PD____ DATE______MOVE the parallel lines and the transversal. Locate 2 pairs of alternate exterior angles and record their measurements: ANGLE MEASUREMENT 3a.

Sketch TWO more pairs of Alternate EXTERIOR Angles below. Accurately, label the angles WITH the appropriate degrees

What do you notice about the alternate exterior angles?

When parallel lines are cut by a transversal, alternate exterior angles formed are______. (ALTERNATE EXTERIOR ANGLES CONJECTURE) NAME ______PD____ DATE______

PART 4: SAME-SIDE INTERIOR ANGLES (A.K.A CONSECUTIVE)

A. Locate 2 pairs of same-side interior angles (A.K.A CONSECUTIVE) and record their measurements: ANGLE MEASUREMENT 1a.

2b. NAME ______PD____ DATE______

B. MOVE the parallel lines and the transversal. Locate 2 pairs of same-side interior angles and record their measurements: ANGLE MEASUREMENT 3a.

Sketch 2 examples of consecutive angles. Be sure to label the angles and include the degrees,

What do you notice about the same-side interior angles?

When parallel lines are cut by a transversal, same-side interior angles (CONSECUTIVE) formed are______. (SAME-SIDE INTERIOR ANGLES CONJECTURE) NAME ______PD____ DATE______

SUMMARY

Corresponding Angles Conjecture: If two parallel lines are cut by a transversal, then the corresponding angles are ______.

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

Alternate Interior Angles Conjecture: If two parallel lines are cut by a transversal, then the alternate interior angles are ______. Conversely, ______.

Alternate Exterior Angles Conjecture: If two parallel lines are cut by a transversal, then the alternate exterior angles are ______. Conversely, ______

Same-Side Interior Angles (CONSECUTIVE ANGLES) Conjecture: If two parallel lines are cut by a transversal, then the same-side interior angles are ______. Conversely, ______NAME ______PD____ DATE______FINAL CHECKS FOR UNDERSTANDING

1 2 3 4 a 5 6 7 8

9 10 11 12 b 13 14 15 16 c d Given a // b, name all angles which are congruent to 4. ______

Given c // d, name all angles which are congruent to 16.______

Given a // b and c // d, name all angles which are congruent to 1.______

a. m ∠ 1 = ______a. m ∠ 1 = ______a. m ∠ 1 = ______

REASON: REASON: REASON: ______

b. m ∠ 2 = _____ b. m ∠ 2 = _____ b. m ∠ 2 = _____

REASON: REASON: REASON: ______NAME ______PD____ DATE______ALGEBRA: Now, try this one. Solve for “x” and the angle:

(x + 10)º