Chapter 3 3-4 Perpendicular Lines

SAT Problem of the day A cube has a surface area of 6x. What is

the volume of the cube? A) B) C) D) E)

Solution to the SAT Problem Right Answer: B

Objectives Prove and apply theorems about

perpendicular lines.

What is the perpendicular bisector? The perpendicular bisector of a

segment is a line perpendicular to a segment at the segment’s midpoint.

Distance from a point to a line 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.

Example#1

A. Name the shortest segment from point A to BC.

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.

Example#1 B. Write and solve an inequality for x.

AC > AP x – 8 > 12

Example#2

A. Name the shortest segment from point A to BC.AB is the shortest segment from A to BC.

B. Write and solve an inequality for x.

AC > AB

12 > x – 5

Student guided practice Do problems 2 and 3 from your book

page175

HYPOTHESISCONCLUSION

Proving perpendicular lines Write a two-column proof.

Given: r || s, 1 2 Prove: r t

solution

Statements Reasons

2. 2 3

3. 1 3 3. Trans. Prop. of

2. Corr. s Post.

1. r || s, 1 2 1. Given

4. r t 4. 2 intersecting lines form lin. pair of s lines .

Proving perpendicular lines Write a two-column proof.

Given:

Prove:

Statements Reasons

2. Conv. of Alt. Int. s Thm.

1. EHF HFG 1. Given

4. Transv. Thm.

3.

4.

2.

Student guided practice Do problem 4 in your book page 175

Homework Do problems 6- 8,12-15 in your book

page 175 and 176

closure Today we learned about perpendicular

lines Next class we learned about slopes of

lines