Parallel Lines and Transversals Angles and parallel lines

• Slides: 19

Parallel Lines and Transversals. Angles and parallel lines. Lesson Objective Video Explore relationships of the angles formed by a transversal cutting parallel lines. Vocabulary Parallel lines, parallel planes, transversal, consecutive interior angels, alternative exterior angels, alternative interior angels, corresponding angels.

Parallel Lines: Coplanar lines that do not intersect. l c x s d w x l

Name all segments that are parallel to H E B A F D Answer: G C

Use the figure to name each of the following. Answer: plane XYZ Answer:

Transversal: A line that intersects two or more lines in a plane at different points. Transversal crossing two lines This transversal crosses two cut across three parallel lines

Transversal and angles transv m k 1 2 m ersal 4 8 NAME 3 5 6 7 k ANGLES 1 2 7 8 3 4 5 6 Consecutive interior angles 3 6 4 5 2 8 Alternate exterior angles 1 7 Alternate interior angles 3 5 4 6 Corresponding angles 1 5 2 6 3 7 4 8 Exterior angles Interior angles

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. m k m 1 3 7 4 6 5 8 1 2 k 3 2 4 @ @ 5 7 6 8

When two parallel lines are cut by a transversal, then…. …. each pair of alternative interior angles is 4 @ 5 congruent. 3 @ 6 …. each pair of alternative exterior angles is 2 @ 7 congruent. 1 @ 8 geogebra …. each pair of consecutive interior angles is 1 2 supplementary. 3 m 4+ m 6=180 m 3+ m 5=180 6 5 7 4 8

In the figure and Find Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution Answer:

In the figure Answer: and Find

Use an auxiliary line. Grid-In Test Item What is the measure of RTV? Read the Test Item Be sure to identify it correctly on the figure.

Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution

Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Addition Postulate Write each digit of 125 in a column of the grid. Then shade in the corresponding bubble in each column.

Grid-In Test Item What is the measure of IGE? K J Answer:

ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate.

Definition of congruent angles Substitution Find y. Subtract x from each side and add 10 to each side. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution

Simplify. Add 100 to each side. Divide each side by 4. Answer:

and ALGEBRA If find x and y. Answer: