1. Bisectors, Medians, Altitudes
Neither you nor the world knows what you can do until you have tried. -- Ralph Waldo Emerson
Bisectors, Medians, Altitudes
Chapter 5 Section 1
Learning Goal: Understand and Draw the 4 special segments of a Triangle

2. Bisectors There are 2 different types of bisectors
(draw the indicated bisector of each figure)
Segment Bisector
A line, segment or ray that cuts a segment in half
Perpendicular Bisector
Angle Bisector
A line, segment or ray that cuts an angle in half

3. Perpendicular Bisector
Given: | Bisector
Show: distance from a point
on the bisector to the endpoints

4. Perpendicular Bisector
If AB is the ḻ bisector of XY, ZY = 8, and ∆ZXY is a right triangle, find XA
If XZ intersects GB, and ZB = 3, what is GZ? X A 6 Y G Z B
Not Enough Information !!!

5. Which Set of Lines demonstrate this Theorem?
Angle Bisector L
Which Set of Lines demonstrate this Theorem? K P M

6. Remember the definition of Distance from a point to a line.
Angle Bisector L
How ‘Bout Now? K
Remember the definition of Distance from a point to a line. P M

7. Angle Bisectors
Find the value of each variable, given the angle bisector.
a =√ 80 y° z°
110° x°
79°
x = 70°
y = 31°
z = 39° 12 12 8 a

8. Draw the medians of the triangles below
A Median is a segment whose endpoints are a vertex and the midpoint of the opposite side of a triangle. y° x°
Draw the medians of the triangles below a b y° x°
Does x = y ??? a b
Does a = b ???

9. Draw the Altitudes for the Triangle How to find the area of a Triangle
The Altitude of a triangle is a segment from a vertex to the line containing the opposite side, and perpendicular to that side.
Draw the Altitudes for the Triangle
Remember:
How to find the area of a Triangle P B
A = ½ b h A

10. Special Segments Identify the Special Segment in the picture 1. 2.

11. Find Every measurement you can
Given an altitude
Given the ḻ bisector
Given an Angle Bisector
Given a
Median
51° 10 10
27°
46°
31° 8
120°
20°

12. Definition of Angle Bisector
Proof
Given: .
Prove:
Proof:
Statements
Reasons
1. Given 2. Angle Sum Theorem 3. Substitution 4. Subtraction Property 5. ____________ 6. Angle Sum Theorem 7. Substitution 8. Subtraction Property
Definition of Angle Bisector

13. Homework Pages 275 – 277; #4 – 8 (even), 11, 13, 22, 26, 36, and 37
(9 problems)