Bisecting Segments and Angles

Section 1.7

Two objects are said to be congruent if they have the same size and shape.

The midpoint of a segment is the point that divides the segment into two congruent segments.

If M is the midpoint of XY , then

XM = MY and XM MY

XM = ½ XY and MY = ½ XY

A bisector of a segment is a line, segment, ray or plane that intersects the segment at its midpoint.

Plane E bisects RT

MN bisects XY , but

XY does not bisect MN

CD bisects EF and

EB bisects CE

G is the midpoint of CE and EB

Solving Two Step Equation Review (see Toolbox page 696)

3x + 9 = 15

3x + 9 – 9 = 15 – 9

3x = 6

3x = 6

3 3

x = 2

MN bisects XY

Find the value of n

	Y

If MN bisects XY, then

XA = AY , then

4n – 6 = 26 (now solve for n)

4n – 6 + 6 = 26 + 6

4n = 32

4n = 32

4 4
n = 8

Coordinates

A pair of numbers used to locate a point on a coordinate plane; the first number tells how far to move horizontally and the second number tells how far to move vertically

Example:

(1,2) represents 1 unit to the right of zero and 2 units up.

What are the coordinates of C?

What is the distance form B to C?

What is the coordinate of the midpoint of BC?

Example:

(1,3) are the coordinates of A.
(^-4,^-3) are the coordinates of B.

Source: http://www.harcourtschool.com/glossary/math2/index6.html

A bisector of an angle is a ray or line that divides the angle into two congruent angles.

The (interior) bisector of an angle is the line or line segment which cuts it into two equal angles on the same "side" as the angle.

Source: http://mathworld.wolfram.com/AngleBisector.html

If EC bisects BED, then:

· m BEC = m CED

· BEC CED

· m BEC = ½ m BED

· m CED = ½ m BED

EC bisects BED

Find the value of x and the m DEC

If EC bisects BED then

m DEC = m BEC

2x –3 = 5x – 15

2x – 2x – 3 = 5x – 2x – 15

– 3 = 3x – 15

– 3 + 15 = 3x – 15 + 15
12 = 3x

12 = 3x

3 3
4 = x

If x = 4 and the m DEC = 5x – 15 , substitute 4 for x in 5x – 15

5x – 15

5 (4) – 15 =
20 –15 =

5^o