### 5.1: Perpendicular and Angle Bisectors

```IT IS….TUESDAY!!!
• Take out your homework and a red pen
• Take out a piece of binder paper and your
whiteboard marker
5.1: Perpendicular and
Angle Bisectors
Learning Objective:
● SWBAT prove and apply theorems about
perpendicular and angle bisectors
Math Joke of the Day
Where do math teachers slip?
Deci-malls (decimals)!
WHITEBOARDS
1. Write and solve an inequality for x.
2x – 3 < 25; x < 14
2. Solve to find x and y in the diagram.
x = 9, y = 4.5
5.1 Perpendicular and Angle Bisectors
Using the root words in equidistant, what do
you picture this word means?
Equidistant
● A point that is the same distance from two
or more objects.
Think - Pair - Share
Fire stations are located at A and B. XY, which
contains Havens Road, represents the
perpendicular bisector of AB .
A fire is reported at point X.
Which fire station is closer
to the fire? Explain.
The city wants to build a
third fire station so that it
is the same distance from
the stations at A and B.
How can the city be sure
Distance and
Perpendicular Bisectors
What do you predict, the Converse of the Perpendicular Bisector Theorem to say?
Example 1:
MN = LN
Example 2:
Find BC
Example 3:
Find TU
Example 4: Applying the Angle Bisector
Theorem
Find BC
Example 5: Applying the Angle Bisector
Theorem
Find the measure:
m<EFH, given that m< EFG
= 50°
Example 5 Applying the Angle
Find m<MKL.
Exit Ticket
Use the diagram for Items 1–2.
1. Given that mABD = 16°,
find mABC.
2. Given that mABD = (2x + 12)° and mCBD =
(6x – 18)°, find mABC.
Use the diagram for Items 3–4.
3. Given that FH is the perpendicular bisector of
EG, EF = 4y – 3, and FG = 6y – 37, find FG.
4. Given that EF = 10.6, EH = 4.3, and FG = 10.6,
find EG.
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