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Holt McDougal Geometry Perpendicular Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal

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Perpendicular LinesHolt GeometryWarm UpLesson PresentationLesson Quiz

Holt McDougal GeometryHolt McDougal GeometryPerpendicular LinesProve and apply theorems about perpendicular lines.ObjectiveHolt McDougal GeometryPerpendicular LinesReview Notes: Perpendicular Lines on pg. 48Complete #1-5 in notes

Holt McDougal GeometryPerpendicular LinesComplete pg. 61 in workbookI reminded you to bring your workbooks everyday

Holt McDougal GeometryPerpendicular LinesComplete your Inbox TaskYou may look for examples on this powerpoint

Holt McDougal GeometryPerpendicular Linesperpendicular bisectordistance from a point to a lineVocabularyHolt McDougal GeometryPerpendicular LinesThe perpendicular bisector of a segment is a line perpendicular to a segment at the segments midpoint. The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line.Holt McDougal GeometryPerpendicular LinesExample 1: Distance From a Point to a Line

The shortest distance from a point to a line is the length of the perpendicular segment, so AP is the shortest segment from A to BC.B. Write and solve an inequality for x.AC > APx 8 > 12x > 20Substitute x 8 for AC and 12 for AP.Add 8 to both sides of the inequality.A. Name the shortest segment from point A to BC.AP is the shortest segment.+ 8+ 8Holt McDougal GeometryPerpendicular LinesCheck It Out! Example 1

The shortest distance from a point to a line is the length of the perpendicular segment, so AB is the shortest segment from A to BC.B. Write and solve an inequality for x.AC > AB12 > x 517 > xSubstitute 12 for AC and x 5 for AB.Add 5 to both sides of the inequality.A. Name the shortest segment from point A to BC.AB is the shortest segment.+ 5+ 5Holt McDougal GeometryPerpendicular Lines

HYPOTHESISCONCLUSIONHolt McDougal GeometryPerpendicular LinesExample 2: Proving Properties of Lines

Write a two-column proof.Given: r || s, 1 2Prove: r t Holt McDougal GeometryPerpendicular LinesExample 2 ContinuedStatementsReasons

2. 2 33. 1 33. Trans. Prop. of 2. Corr. s Post.1. r || s, 1 21. Given4. r t 4. 2 intersecting lines form lin. pair of s lines .Holt McDougal GeometryPerpendicular LinesCheck It Out! Example 2

Write a two-column proof.Given: Prove:

Holt McDougal GeometryPerpendicular LinesCheck It Out! Example 2 ContinuedStatementsReasons 3. Given2. Conv. of Alt. Int. s Thm.1. EHF HFG1. Given4. Transv. Thm.3.

4.

2.

Holt McDougal GeometryPerpendicular LinesExample 3: Carpentry Application

A carpenters square forms aright angle. A carpenter places the square so that one side isparallel to an edge of a board, and then draws a line along the other side of the square. Then he slides the square to the right and draws a second line. Why must the two lines be parallel?

Both lines are perpendicular to the edge of the board. If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other, so the lines must be parallel to each other.Holt McDougal GeometryPerpendicular LinesCheck It Out! Example 3 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?

Holt McDougal GeometryPerpendicular LinesCheck It Out! Example 3 ContinuedThe shoreline and the path of the swimmer should both be to the current, so they should be || to each other.

Holt McDougal GeometryPerpendicular Lines

Lesson Quiz: Part II3. Complete the two-column proof below.Given: 1 2, p qProve: p rProofStatementsReasons1. 1 21. Given2. q || r3. p q4. p r2. Conv. Of Corr. s Post.3. Given4. Transv. Thm.Holt McDougal GeometryPerpendicular Lines20