Happy Monday 
• Begin your Entry Ticket as soon as you get your
quiz back!
Tonight’s HW:
• P 175 #1-3, 5-7, 9-14.16- 21, 24
• Bring your compass, protractor and ruler to the
next class!
3 Things
Classroom Jobs
Paper Passer
Date Keeper ( Per 1 only)
Quiz #3
•
•
•
•
A= 22.5- 25
B= 20- 22
C= 17.5- 19.5
Below a 17.5 please come see me during
tutorial! 
3.4: Perpendicular Lines
Learning Objective:
SWBAT prove and apply theorems
about perpendicular lines.
Math Joke of the Day…
Why is the angle formed by two perpendicular
lines never wrong?
Because it’s always right!
APK…
• What is a bisector?
– Think-pair-share
Discuss with your table:
• What do you think a perpendicular bisector
is?
Perpendicular Lines (3.4)
Perpendicular Bisector
o A line that creates a right angle (90°) to a segment at the
segment’s midpoint.
Distance from a point to a line
o The shortest segment from a point to a line is perpendicular to the
line.
Inequality Practice
Red Flag Alert
When you multiply
or divide by a
negative number,
you need to FLIP the
inequality sign!
Whiteboards!!
Before we move on to our lesson for the period I need to make sure you
are comfortable with inequalities.
Perpendicular Lines (3.4)
We will do the first problem together!
Whiteboards
A. Name the shortest segment from point A to BC.
AB
B. Write and solve an inequality for x.
AC > AB
12 > x – 5
+5
+5
17 > x
AB is the shortest segment.
Substitute 12 for AC and x – 5 for AB.
Add 5 to both sides of the inequality.
Whiteboards!!
Lets now discuss problems with special angle pairs and perpendicular
lines.
Think – Table - Share
1. Sketch two intersecting lines that create a linear pair of congruent
angles.
2. What is the degree of these congruent angles?
Theorem
HYPOTHESIS
CONCLUSION
What If…?
• A transversal is perpendicular to one of the
parallel lines.
– What do you think would be the case for the other
parallel line?
– Draw it on your whiteboards
Perpendicular Transversal Theorem
Example 3
Solve for x and y
What About…?
If two lines are perpendicular to the same line?
Think-pair- share
You Got It!
They are parallel
Four Corners!
The Four Corners National Monument is at the intersection of the
borders of Arizona, Colorado, New Mexico, and Utah. It is called
the four corners because the intersecting borders are perpendicular.
If you were to lie down on the intersection, you could be in four states
at the same time—the only place in the United States where this is
possible. The figure shows the Colorado-Utah border extending north
in a straight line until it intersects the Wyoming border at a right angle.
Explain why the Colorado-Wyoming border must be parallel to the
Colorado–New Mexico border
Exit Ticket: Do on the back of your Entry Ticket
1. Write and solve an inequality for x.
2x – 3 < 25; x < 14