Honors Math 3 Unit 1: Geometry Term Review
Word Box:
Vocabulary
Definition of Linear Pair,
Vertical angles,
Definition
If B is between A and C,
then AB + BC = AC
A
2x
B
5
C
11
2x + 5 = 11 so 2x = 6
x= 3
PART + PART = TOTAL
Name: ___________________________________________
Segment Addition postulate , Definition of midpoint,
Complementary angles,
Angle addition Postulate,
Angle bisector,
Supplementary angles
Worked Out Example
Practice Example
Examples
D is between A and M. AD = 2x + 3. P is between M and A.
Y is between X and Z.
DM = 3x + 4
AM = 6x +2.
PA = 6x + 5
PM = 3x + 2
XY = 4x-1 ,YZ = 3x+7, and
Find x and AD
MA = 10x + 2.
XZ = 10x -12. Find x and YZ.
A
D
M
Find x and PM
AD + DM = AM
2x + 3 + 3x + 4 = 6x + 2
5x + 7 = 6x + 2
5 =x
AD= 2x + 3 = 2(5) + 3 = 13
If M is the midpoint of AB,
then AM = BM and AM = ½ AB
If ray AP is on the interior
of  CAB then
m  CAP + m  PAB = m  CAB
C
P
A
M is the midpoint of AB. AB = 22.
AM = 7x – 3. Find x and MB
7x – 3
AM = ½ AB
A
M
B
7x – 3 = ½ (22)
7x – 3 = 11
22
7x = 14
x=2
MB = AM = 7(2) – 3 = 11
Ray CD is in the interior of  ACB.
m  ACD = 3x + 5. m  DCB = 4x – 2
m  ACB = 8x – 3. Find x and m  ACD
A
C
m  MAP = m  PAT
= ½ m  MAT
T is the midpoint of SV.
ST = 3x-2 and SV = 10x-22.
Find x and TV.
Ray PM is in the interior of
 APT.
m  APM = 3x + 8 m  APT = 10x - 3
m  MPT = 5x – 3.
Find x and m  APT
Ray BD is in the interior of
<ABC. m<ABD = 5x +3, m<DBC
= 18-x, and m<ABC = 2x+41.
Find x and m<ABD
Ray AL bisects
Ray BD bisects <ABC.
m<ABC = 12x -4, m<DBC = 4x
+10. Find x and m<ABD.
B
m  ACD + m  DCB = m  ACB
3x + 5 + 4x – 2 = 8x – 3
7x + 3 = 8x – 3
6=x
m  ACD = 3x+5 = 3(6)+5 = 23
B
If ray AP bisects  MAT, then
D
D is the midpoint of AM.
AD = 4x + 8. AM = 12x + 8.
Find x and DM.
Ray PT bisects APC.
m  APT = 4x + 2 m  APC = 6x + 20.
Find x and m  PTC
A
T
m  APT = ½ m  APC
P
<multiply by 2>
C 4x + 2 = ½ (6x + 20)
8x + 4 = 6x + 20
2x = 16
x = 8 so m  PTC=4(8) +2 = 34o
 CAT.
m  CAT = 7x – 5 m  LAT = 2x + 2.
Find x and m  CAL.
Vocabulary
Definition
If two angles are complementary
then the two angles add up to
90o
If  1 and  2 are complementary
then m  1 + m  2 = 90o
If two angles are supplementary
then the two angles add up to
180o .
If  1 and  2 are supplementary
then m  1 + m  2 = 180o
Two angles that are
supplementary and adjacent
(ADDS UP TO 180o)
Worked Out Example
Practice Example
Examples
 ABC and  CBD are complementary.
m  ABC = 2x2 + 3. m  CBD = 15o. Find x
 1 and  2 are complementary.
m  1 = 4x2 + 20. m  2 = x2 + 50.
Find x and the measure of the larger
angle.
 3 and  4 are complementary.
m  3 = 8x+3, m  4 = 5x+9. Find x
and the smaller angle.
 1 and  2 are supplementary.
They are in the ratio of 1:5. Find the
m2
 3 and  4 are supplementary
angles. They are in a ratio of 5:7.
Find m  3.
Two angles make a linear pair. The
larger angle is 30 less than six times
the smaller angle. Find the measure
of the larger angle.
Two angles make a linear pair.
The larger is 30 more than twice
the smaller. Find the measure of
the smaller angle.
 1 and  2 are vertical angles.
m  1 = 4x2 + 10 m  2 = 110.
Find x and m  1
 3 and  4 are vertical angles.
m  3 = 115, m  4 = 5x2-10.
Find x and m  3.
2x2 + 3 + 15 = 90
2x2 + 18 = 90
2x2 = 72
x2 = 36
x = √36 = 6.
 ABC and  CBD are supplementary
and are in the ratio of 5:13. Find the
measure of the largest angle.
m  ABC + m  CBD = 180o
m  ABC = 5x and m  CBD = 13x
5x + 13x = 180
18x = 180
x = 10
Largest=13x = 13(10) = 130o
Two angles make a linear pair. The
larger angle is 12 less than five times
the smaller angle. Find the measure of
the larger angle.
Small + Large = 180
x + 5x – 12 = 180
6x – 12 = 180
6x = 192
x = 32. Large=5(32)-12 = 148o
x + y = 180o
m1 = m3
1
3
m2 = m4
2
4
OPPOSITE ANGLES ARE
CONGRUENT
Solve for x
x + 16 = 4x – 5
16 = 3x – 5
21 = 3x
7=x