1. BellWork MA.912.D.6.2 and 6.3
Which of the following is the converse of the following statement?
“If an animal is a crow, then it has wings.”
If an animal is not a crow, then it does not have wings.
If an animal has wings, then it is a crow.
If an animal does not have wings, then it is not a crow
Which of the following is the contrapositive of the following statement?
“If an animal is a loggerhead sea turtle, then its expected life span is approximately 70 years.”
If an animal has an expected life span of approximately 70 years, then it is a loggerhead sea turtle.
If an animal is not a sea turtle, then its expected life span is not approximately 70 years.
If an animal does not have an expected life span of approximately 70 years, then it is a loggerhead sea turtle.
If an animal does not have an expected life span of approximately 70 years, then it is not a loggerhead sea turtle

2. 5.2 Perpendicular and Angle Bisector
Geometry: Chapter 5 Relationships within Triangles

3. Review
Now, we can identify corresponding parts of congruent triangles by visualizing the figures placed on top of each other.
We can show two triangles are congruent by proving that certain relationships exist between three pairs of corresponding parts.
You can tell whether a triangle is isosceles or equilateral by looking at the number of congruent angles or sides.

4. Lesson’s Purpose
Objective
Essential Question
To use properties of perpendicular bisectors and angle bisectors.
What are properties of an angle and perpendicular bisector?
Perpendicular bisector indicates the shortest distance from a point on a line
If a point is on the Angle bisector then it is equidistant from the sides of the angle.
A point on the perpendicular bisector is equidistant from the endpoints of the segment.

5. Perpendicular Bisector
Equidistant- a point from two objects if it is the same distant from the objects.
Definition of Perpendicular Bisector
Perpendicular Bisector is a perpendicular line or a segment that passes through the midpoint of a line.
A perpendicular bisector divides a line segment into two equal segments.

6. Using Perpendicular Bisector
Solution
Example of Perpendicular Bisector
Step 1: A perpendicular bisector divides a line segment into two equal parts.
Step 2: The length of AB is 12 cm and CD is the perpendicular bisector of AB.
Step 3: So, AO = OB =AB/2 =12/2 = 6 [Substitute AB = 12.]
Step 4: AO = OB = 6 cm
AB is a line segment of length 12 cm. CD is the perpendicular bisector of AB. Find the length of AO and OB.

7. Perpendicular Bisector
Regular Theorem :
If AO PQ and OP=OB, Then AP=AQ
Converse Theorem: If AP=AQ, then AO PQ and OP=OB

8. Examples
What is the value of x?
X=5
X=6
X=8
X=1
X=4
X=2

9. Using Perpendicular Theorem
Solution
AB=BD
9x-2=7x+10
9x(-7x)-2=7x(-7x)+10
2x-2(+2)=10(+2)
2x=12
X=6

10. Examples What is the relationship between LN and MO?
What is the value of x?
What is LN?
What is MO?
Solution
LM is the perpendicular bisector of MO
X=10
LM=50
LO=50

11. Angle Bisector Theorem
Regular Theorem
Converse Theorem
If… AD bisects BAC, DC AC, DBAB. Then…DC=DB
If ….DC BC, DA BA, and DA=DC then… BD bisects ABC

12. Practice Examples 7x+17=(3(4x-1)) 7x+17=12x-3 20=12x-7x 20=5x X=4

13. Examples
What is the value of x?
X=10
X=70
X=40
X=4

14. Examples
Find TS?
Find SU?
Find UV?
From the information given in the figure, how is TU related to SU?
TS=3.7
SU=6
UV=7.9

15. Examples
Find x, BA, DA?
Find p,IJ,KJ?
X=2, BA=DA=7
p=3, IJ=KJ=15

16. Real World Connection

17. Summary
Perpendicular Bisector
Angle Bisector
Perpendicular bisectors indicate the shortest distance from a point to a line.
If a point is on an angle bisector, then the point is equidistant from the sides of the angle.

18. Ticket Out and Homework
Sec 5.2-
Pg #'s 6-23
What statement describes the points on a perpendicular and angle bisector?
They are equidistant from the segment and angle.