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Math 1
Review—Unit 3
Name ____________________________________
Period ___________ A or B?__________
Standard: Angles
MM1G. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
_________________1. The sides of a triangle are 15, 8 and x. What are the possible values for x?
_________________2. In CAT , m C is 51 and m T is 63. What is the longest side of the triangle?
__________________3. Two sides of a triangle have lengths 3 and 12. The possible lengths of the third side are ______ .
__________________4. Write the angles in order from largest to smallest.
B
9
6
A
_________________5.
C
7
Find the measure of x.
80
130
x
Open response. Answer each of the questions, fully and accurately.
6.
Draw triangle PHS and label the angles accordingly: mN  98, mH  65. Find the missing angle. Then
list the sides in order from least to greatest.
______ , _______ , _______
7.
Draw triangle XYZ and label the sides accordingly. XY = 22, YZ = 42, XZ = 31. List the angles in order from
least to greatest.
_______ , _______ , ______
Standard: Triangle Congruence
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
Pictures may not be drawn to scale.
________1.
How do you know the triangles are congruent? Write a congruence X
Statement.
I
W
Y
A
________2.
E is the midpoint of AC and BD . How do you know the triangles
are congruent? Write a congruence statement.
E
D
B
A
C
________3.
What are the five ways (short cuts) to prove the two triangles are congruent?
________4.
If
________5.
Given Q  V and the figure shown, which two triangles can you prove are congruent?
ABC  RST then R  _____.
V
Q
Write a congruence statement.
M
A
Definitions
6. Congruent figures
7. Hypotenuse
8. Legs
9. Included angle
10. Included side
W
Decide whether enough information is given to prove that the triangles are congruent. If there is enough
information, state the congruence postulate or theorem you would use. (SSS, SAS, ASA, AAS, HL)
11
12
13
14
Answer_____________
15
Answer_____________
16
Answer_____________
Answer_____________
Answer_____________
Answer_____________
Standard: Points of Concurrency
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.
________1. Which points of concurrency may lie outside the triangle?
_______2. Which points of concurrency are always inside the triangle?
_______3. Which point of concurrency is equidistant from the vertices of the triangle?
_______4. Which point of concurrency is equidistant from the sides of the triangle?
Name the special segment drawn.
_______________________6.
_______________________7.
_______________________8.
_______________________9.
What is the point of concurrency for the:
______________________10. altitudes
______________________11. angle bisectors
______________________12. medians
______________________13. perpendicular bisectors
MM1G3 Review Unit 3 Angles and Parallelograms
1. How do you find the sum of the interior angles of a polygon? Exterior angles of a polygon?
2. In a parallelogram, opposite sides are ____. (definition)
In a parallelogram, opposite sides are ____.
In a parallelogram, opposite angles are _____.
In a parallelogram, consecutive angles are _____, which means _____.
In a parallelogram, diagonals ______.
3. The ways to prove that a quadrilateral is a parallelogram are:
_____ pair(s) of opposite sides are _____. (definition)
_____ pair(s) of opposite sides are _____.
_____ pair(s) of opposite angles are _____.
_____ pair(s) of opposite sides are _____ and _____.
The diagonals ___________.
5. Find the sum of measures of the interior angles of a convex 40-gon.
6. Find the measure of one interior angle of a regular 18-gon.
7. Find the measure of one exterior angle of a nonagon.
Use the following diagram .
8. Find m  HJF
11
9. Find GK
123o
9
24
10. Find FJ
37
9
11. Find m  GFJ
12. The figure below is a parallelogram. Find x and y.
x+6
7y – 3
4y + 15
-3x – 8
13. Each interior angle of a regular polygon measures 168o. What type of polygon is it?
14. Find x.
61o
62o
69o
xo
48o
33o
MM1G3 Review Unit 3 Angles and Parallelograms
1. How do you find the sum of the interior angles of a polygon? Exterior angles of a polygon?
2. In a parallelogram, opposite sides are ____. (definition)
In a parallelogram, opposite sides are ____.
In a parallelogram, opposite angles are _____.
In a parallelogram, consecutive angles are _____, which means _____.
In a parallelogram, diagonals ______.
3. The ways to prove that a quadrilateral is a parallelogram are:
_____ pair(s) of opposite sides are _____. (definition)
_____ pair(s) of opposite sides are _____.
_____ pair(s) of opposite angles are _____.
_____ pair(s) of opposite sides are _____ and _____.
The diagonals ___________.
5. Find the sum of measures of the interior angles of a convex 40-gon.
6. Find the measure of one interior angle of a regular 18-gon.
7. Find the measure of one exterior angle of a nonagon.
Use the following diagram .
8. Find m  HJF
11
9. Find GK
123o
9
10. Find FJ
24
37
9
11. Find m  GFJ
12. The figure below is a parallelogram. Find x and y.
x+6
7y – 3
4y + 15
-3x – 8
13. Each interior angle of a regular polygon measures 168o. What type of polygon is it?
14. Find x.
61o
62o
69o
xo
48o
33o
MM1G3d Review for Quadrilaterals
Name__________________
Understand, use, and prove properties of and relationships among
special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, kite.
1. A _______ is an equilateral parallelogram.
2. A _______ is an equiangular parallelogram.
3. A _____ is an equilateral and equiangular quadrilateral.
4. A _____ is a quadrilateral with exactly one pair of parallel sides.
5. A _____ is a quadrilateral with two pairs of parallel sides.
6. A _____ is a quadrilateral with exactly one pair of opposite angles that are congruent.
Answer each question completely.
Use the diagram below to answer questions . KLMN is a rectangle. KL = 12, KM = 9
K
L
(10x – 50)o
M 7. Find the value of x.
N
8. Find MN.
9. Find KN.
10. ABCD is a trapezoid.
Find the measure of  A
A
B
D
112o
C
11. m  K =_______
K
111o I
E
37o
T