Perpendicular Lines Unit 2-4. Warm Up Solve each inequality. 1. x – 5 < 8 2. 3x + 1 < x Solve each equation. 3. 5y = 90 4. 5x + 15 = 90 Solve the systems.

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Presentation transcript:

Perpendicular Lines Unit 2-4

Warm Up Solve each inequality. 1. x – 5 < x + 1 < x Solve each equation. 3. 5y = x + 15 = 90 Solve the systems of equations. 5.

The ______________________ of a segment is a line perpendicular to a segment at the segment’s midpoint. Vocabulary Words perpendicular bisector The shortest segment from a point to a line is _________________ to the line. This fact is used to define the _________ _______________________________ as the length of the perpendicular segment from the point to the line. perpendicular distance from a point to a line

A. Name the shortest segment from point A to BC. Example 1: Distance From a Point to a Line B. Write and solve an inequality for x. AC > AP AP is the shortest segment. x – 8 > 12 Substitute x – 8 for AC and 12 for AP. + 8 Add 8 to both sides of the inequality. x > 20

HYPOTHESISCONCLUSION

Example 2: Proving Properties of Lines Write a two-column proof. Given: r || s, 1  2 Prove: r  t StatementsReasons 1. r || s, 1  2 1. Given 2. 2  3 2. Corr. s Post. 3. 1  3 3. Trans. Prop. of  4.4. Supplementary angles 1 + 3 = 1 and 3 = Equal angles that are supplementary must each = 90 o 6. r  t 6. Definition of perpendicular

A swimmer who gets caught in a rip current should swim in a direction perpendicular to the current. Why should the path of the swimmer be parallel to the shoreline? Word Problem Example The shoreline and the path of the swimmer should both be  to the current, so they should be || to each other.

On your own: Examples 1. Write and solve an inequality for x. 2. Solve to find x and y in the diagram.