20 DIFFERENT SKILLS AND TOPICS THAT STUDENTS SHOULD BE PROFICIENT IN BEFORE ENTERING GEOMETRY
GETTING READY FOR
TABLE OF CONTENTSPAGE TOPIC
1 THE NUMBER PROPERTIES
2 CALCULATING SLOPE
3 GRAPHING IN SLOPE-INTERCEPT FORM
4 DETERMINING PARALLEL AND PERPENDICULAR LINES
5 SOLVING MULTI-STEP EQUATIONS
6 SOLVING INEQUALITIES
7 SUBSTITUTION TO SOLVE SYSTEMS OF EQUATIONS
8 FACTORING TRINOMIALS
9 SIMPLIFYING RADICALS
10 OPERATIONS WITH RADICALS
11 CLASSIFYING SEGMENTS, RAYS, and LINES
12 NUMBER OF EDGES & VERTICES
13 ANGLE MEASUREMENTS
14 TYPES OF TRIANGLES
15 TYPES OF QUADRILATERALS
16 PARTS OF A CIRCLE
17 AREA FORMULAS OF BASIC SHAPES
18 VOLUME FORMULAS OF BASIC FIGURES
19 BASIC TRANSFORMATIONS
20 CONGRUENT OR SIMILAR
@iteachalgebra
THE NUMBER PROPERTIES1
@iteachalgebra
Match each expression with the property that it shows.
5 + 0 = 5
Additive Identity
5(1) = 5
Multiplicative Identity
5(0) = 0
Zero Product Property
2 + 3 = 3 + 2
Commutative Property
of Addition
2(3) = 3(2)Commutative Property
of Multiplication
2 + (3 + 4) = (2 + 3) + 4
Associative Property
of Addition
2(3•4) = (2•3)4
Associative Property
of Multiplication
3(2 + 5) = 6 + 15
Distributive Property
CALCULATING SLOPE2
@iteachalgebra
Find the slope between the given points or on the graph.
(1, 3) and (5, 8) (-2, 7) and (5, 4) (1, -3) and (0, 8)
(-1, -9) and (4, 0) (-8, 8) and (-2, 8) (-4, 9) and (-4, -8)
GRAPHING IN SLOPE-INTERCEPT FORM
3
@iteachalgebra
y = x + 3 y = x - 1
y = -2x y = -x + 3
y = 1
2x - 4 y = −
3
2x + 1
y = 2x + 3
y = -3x + 3
y =4
3x - 3
PARALLEL & PERPENDICULAR4
@iteachalgebra
Circle whether each pair of equations is parallel, perpendicular, or neither.
y = x + 3
y = x - 2{slope:
parallel perpendicular neither
y = 2x + 3
2x – y = 4{slope:
parallel perpendicular neither
y = -x
y = x + 4{slope:
parallel perpendicular neither
y = 3x + 3
x – 3y = 9{slope:
parallel perpendicular neither
2x + 3y = 6
3x - 2y = 4{slope:
parallel perpendicular neither
y = 2
5x + 3
2x – 5y = 10{slope:
parallel perpendicular neither
4x + y = 6
y = -4x - 2{slope:
parallel perpendicular neither
y = 5x + 3
x + 4y = 8{slope:
parallel perpendicular neither
SOLVING MULTI-STEP EQUATIONS
5
@iteachalgebra
Solve each equation. Simplify your answer.
3(x + 4) = 2.5(x – 6) 2(x - 5) + 7 = -3(2x – 6)
1
2(4x - 8) =
3
4(8x + 4)
1
2x + 5 =
2
5x - 8
2
3(5x + 6) =
3
2(8x - 4)
1
3x +
1
4=
2
3x -
1
6
SOLVING INEQUALITIES6
@iteachalgebra
Solve the inequalities.
30 + 2x < 17 15 < -4x + 18 6 ≤ 4x + 80
10 - 2x ≤ 17 -12 > -3x - 12 -9 ≤ -5x - 33
8 + 2x < -x + 17 4x - 9 ≤ 5x + 80
5 - 2x 6(x – 3) -3(3 + x) ≤ -6x - 11
SUBSTITUTION TO SOLVE SYSTEMS
7
@iteachalgebra
Solve each system by substitution.
y = -2x
y = x + 3{ y = 3x + 3
x – 3y = 9{
2x + y = 6
x = 2y - 1{ y = 2
5x + 3
2x – 5y = 10{
x = -4
y = 5{ 2x + 3y = 6
y = -3x - 1{
FACTORING TRINOMIALS 8
@iteachalgebra
Factor each trinomial.
Solve the polynomial equation.
x2 + 5x + 4 x2 + 8x + 16 x2 - 6x + 8
x2 - 6x - 7 x2 + 5x + 6 x2 - 10x + 25
2x2 + 7x + 3 3x2 - 13x + 4 5x2 + 7x - 6
x2 + 9x = -8 2x2 = 7x - 3 3x2 + 15x = -18
SIMPLIFYING RADICALS9
@iteachalgebra
Simplify each radical expression.
4 6 8 9 10
12 18 25 28 32
40 48 50 55 60
64 72 90 99 120
150 160 200 256 300
OPERATIONS WITH RADICALS10
@iteachalgebra
Simplify each radical expression.
2 + 2 4 3 + 3 5 6 + 2 6
2 - 2 4 3 - 3 5 6 - 2 6
2 • 2 4 3 • 3 5 6 • 2 6
72 + 50 4 45 - 125 5 27 + 2 5
CLASSIFYING SEGMENTS, RAYS, & LINES
11
@iteachalgebra
Determine the segments, rays, and lines from the diagram.
SEGMENTS RAYS LINES
A
B
CD
Determine whether each statement is true or false.
Two lines can intersect at exactly one point.
Two lines can intersect at exactly two points.
The are an infinite number of points on a line.
A ray has an arrow at one end.
A segment and a line are identical.
NUMBER OF EDGES & VERTICES12
@iteachalgebra
List the number of edges and vertices for each figure.
edges:
vertices:
edges:
vertices:
edges:
vertices:
rectangular prism
square pyramid
cylinder
ANGLE MEASUREMENTS13
@iteachalgebra
Circle the type of angle shown and the best approximate measure of the angle.
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
TYPES OF TRIANGLES14
@iteachalgebra
Name the triangle based on its sides and angles.
Names include equilateral, isosceles, and scalene, acute, obtuse, and right.
60
60 6090
60 30
120
30 30
45
4590
40
70
70
55
8045
TYPES OF QUADRILATERALS15
@iteachalgebra
Determine if the quadrilateral is a square, rectangle, rhombus, trapezoid,
isosceles trapezoid, parallelogram, or more than one of those names.
>
>
>
>
>
>
> >
PARTS OF A CIRCLE16
@iteachalgebra
Given the circle, name each part.
Find the circumference and area of each circle.
5
8
Circumference: C = 2𝜋r Area: A = 𝜋r2
Circumference: C = 𝜋d Area: A = 𝜋r2
AREA FORMULAS17
@iteachalgebra
Calculate the area of each figure.
A = lw
13.5
4
10
3
A = 1
2bh
16
9.8
A = bh
rectangle triangle
parallelogram
A = 1
2h(b1 + b2)
trapezoid
5
9
4
VOLUME FORMULAS18
@iteachalgebra
Calculate the volume of each figure.
V = s3 V = lwh
V = r2h
cube rectangular prism
cylinder
V = 4
3r3
sphere
4
3
5
6
6
6
5
4
8.5
TRANSFORMATIONS19
@iteachalgebra
Determine the type of transformation shown in each diagram as a translation,
rotation, reflection, or dilation.
CONGRUENT OR SIMILAR20
@iteachalgebra
Determine whether the figures shown are congruent or similar.
ANSWERKEY
THE NUMBER PROPERTIES1
@iteachalgebra
Match each expression with the property that it shows.
5 + 0 = 5
Additive Identity
5(1) = 5
Multiplicative Identity
5(0) = 0
Zero Product Property
2 + 3 = 3 + 2
Commutative Property
of Addition
2(3) = 3(2)Commutative Property
of Multiplication
2 + (3 + 4) = (2 + 3) + 4
Associative Property
of Addition
2(3•4) = (2•3)4
Associative Property
of Multiplication
3(2 + 5) = 6 + 15
Distributive Property
ANSWER KEY
CALCULATING SLOPE2
@iteachalgebra
Find the slope between the given points or on the graph.
(1, 3) and (5, 8) (-2, 7) and (5, 4) (1, -3) and (0, 8)
(-1, -9) and (4, 0) (-8, 8) and (-2, 8) (-4, 9) and (-4, -8)
m = 8 − 3
5 − 1= 5
4m =
4 − 7
5 −(−2)= −3
7 m = 8 −(−3)
0 − 1= 11
−1
m = -11
m = 0 −(−9)
4 −(−1)= 9
5m =
8 − 8
−2 −(−8)= 0
6
m = 0
m = −8 − 9
−4 −(−4)= −17
0
m = undefined
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛= 2
1= 2
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛= −1
3
2
1
-1
3
ANSWER KEY
GRAPHING IN SLOPE-INTERCEPT FORM
3
@iteachalgebra
y = x + 3 y = x - 1
y = -2x y = -x + 3
y = 1
2x - 4 y = −
3
2x + 1
y = 2x + 3
y = -3x + 3
y = 4
3x - 3
ANSWER KEY
PARALLEL & PERPENDICULAR4
@iteachalgebra
Circle whether each pair of equations is parallel, perpendicular, or neither.
y = x + 3
y = x - 2{slope:
parallel perpendicular neither
y = 2x + 3
2x – y = 4{slope:
parallel perpendicular neither
y = -x
y = x + 4{slope:
parallel perpendicular neither
y = 3x + 3
x – 3y = 9{slope:
parallel perpendicular neither
2x + 3y = 6
3x - 2y = 4{slope:
parallel perpendicular neither
y = 2
5x + 3
2x – 5y = 10{slope:
parallel perpendicular neither
4x + y = 6
y = -4x - 2{slope:
parallel perpendicular neither
y = 5x + 3
x + 4y = 8{slope:
parallel perpendicular neither
m = 1
m = 1
m = 2
m = 2
m = -1
m = 1
m = 3
m = 1
3
m = −2
3
m = 3
2
m = 2
5
m = 2
5
m = -4
m = -4
m = 5
m = −1
4
ANSWER KEY
SOLVING MULTI-STEP EQUATIONS
5
@iteachalgebra
Solve each equation. Simplify your answer.
3(x + 4) = 2.5(x – 6) 2(x - 5) + 7 = -3(2x – 6)
1
2(4x - 8) =
3
4(8x + 4)
1
2x + 5 =
2
5x - 8
2
3(5x + 6) =
3
2(8x - 4)
1
3x +
1
4=
2
3x -
1
6
ANSWER KEY
3x + 12 = 2.5x – 15-2.5x -2.5x
0.5x + 12 = – 15-12 = – 12
0.5x = – 270.5 0.5
x = -54
2x - 10 + 7 = -6x + 18
2x - 3 = -6x + 18 + 6x + 6x
8x - 3 = 18 + 3 + 3
8x = 21
8 8 x = 2.625
2x – 4 = 6x + 1-2x -2x
– 4 = 4x + 1- 1 - 1
– 5 = 4x
4 4
-1.25 = x
10(1
2x + 5) = 10(
2
5x – 8)
5x + 50 = 4x - 80-4x -4x
x + 50 = - 80- 50 - 50
x = - 130
6[2
3(5x + 6)] = 6[
3
2(8x - 4)]
4(5x + 6) = 9(8x - 4)
20x + 24 = 72x - 36-72x -72x
-52x + 24 = - 36- 24 = - 24
-52x = - 60-52 -52
x = 15
13
12(1
3x +
1
4) = 12(
2
3x -
1
6)
4x + 3 = 8x - 2-4x -4x
3 = 4x - 2+ 2 + 2
5 = 4x4 4
1.25 = x
SOLVING INEQUALITIES6
@iteachalgebra
Solve the inequalities.
30 + 2x < 17 15 < -4x + 18 6 ≤ 4x + 80
10 - 2x ≤ 17 -12 > -3x - 12 -9 ≤ -5x - 33
8 + 2x < -x + 17 4x - 9 ≤ 5x + 80
5 - 2x 6(x – 3) -3(3 + x) ≤ -6x - 11
ANSWER KEY
-30 -30
2x < -132 2
x < -6.5
- 18 - 18
-3 < -4x-4 -43
4> x x <
3
4
- 80 - 80
-74 ≤ 4x4 4
-19 ≤ x x -19
-10 -10
-2x ≤ 7-2 -2
x -3.5
+12 +12
0 > -3x-3 -3
0 < x x > 0
+33 +33
24 ≤ -5x-5 -5
-4.8 x x ≤ -4.8
-8 -8
2x < -x + 9+x +x
3x < 9
x < 3
-4x -4x
- 9 ≤ x + 80-80 - 80
- 89 ≤ x
x - 89
5 - 2x 6x - 18-5 -5
- 2x 6x - 23- 6x - 6x- 8x - 23- 8 - 8
x ≤ 2.875
-9 – 3x ≤ -6x - 11+9 + 9
– 3x ≤ -6x - 2+ 6x + 6x
3x ≤ - 23 3
x ≤ -2
3
SUBSTITUTION TO SOLVE SYSTEMS
7
@iteachalgebra
Solve each system by substitution.
y = -2x
y = x + 3{ y = 3x + 3
x – 3y = 9{
2x + y = 6
x = 2y - 1{ y = 2
5x + 3
2x – 5y = 10{
x = -4
y = 5{ 2x + 3y = 6
y = -3x - 1{
ANSWER KEY
-2x = x + 3-x -x
-3x = 3
x = -1
y = -2x
y = -2(-1)
y = 2
(-1, 2)
x – 3(3x + 3) = 9x – 9x – 9 = 9
-8x – 9 = 9
-8x = 18
x = -2.25
y = 3x + 3
y = 3(-2.25) + 3
y = -6.75 + 3
y = -3.75
(-2.25, -3.75)
2(2y – 1) + y = 6
4y – 2 + y = 6
5y = 8
y = 1.6
x = 2y - 1
x = 2(1.6) - 1
x = 3.2 - 1
x = 2.2
(-4, 5)
2x – 5(2
5x + 3) = 10
2x – 2x + 15 = 10
15 = 10
no solution(2.2, 1.6)
2x + 3(-3x – 1) = 6
2x – 9x – 3 = 6
-7x – 3 = 6
-7x = 9
x = −9
7
y = -3x - 1
y = -3(−9
7)- 1
y = 27
7- 1
y = 20
7
(−9
7, 20
7)
FACTORING TRINOMIALS 8
@iteachalgebra
Factor each trinomial.
Solve the polynomial equation.
x2 + 5x + 4 x2 + 8x + 16 x2 - 6x + 8
x2 - 6x - 7 x2 + 5x + 6 x2 - 10x + 25
2x2 + 7x + 3 3x2 - 13x + 4 5x2 + 7x - 6
x2 + 9x = -8 2x2 = 7x - 3 3x2 + 15x = -18
ANSWER KEY
(x + 1)(x + 4)
(x + 1)(x - 7)
(x + 4)(x + 4)
(x + 4)2
(x - 2)(x - 4)
(x + 2)(x + 3) (x - 5)(x - 5)
(x - 5)2
(2x + 1)(x + 3) (3x - 1)(x - 4) (5x - 3)(x + 2)
x2 + 9x + 8 = 0
(x + 1)(x + 8) = 0
x + 1 = 0 x + 8 = 0- 1 - 1 - 8 - 8
x = -1 x = -8
2x2 - 7x + 3 = 0
(2x – 1)(x – 3) = 0
2x – 1 = 0 x - 3= 0+ 1 + 1 +3 +3
2x = 1 x = 3
x = {-8, -1}2 2
x = {1
2, 3}
3x2 + 15x + 18 = 0
3(x2 + 5x + 6) = 0
3(x + 2)(x + 3) = 0
x + 2 = 0 x + 3 = 0
- 2 - 2 - 3 - 3
x = -2 x = -3
x = {-3, -2}
SIMPLIFYING RADICALS9
@iteachalgebra
Simplify each radical expression.
4 6 8 9 10
12 18 25 28 32
40 48 50 55 60
64 72 90 99 120
150 160 200 256 300
ANSWER KEY
2 6 4 2
2 2
3 10
4 3
2 3
9 2
3 2
4 7
2 7
5 16 2
4 2
4 10
2 10
16 3
4 3
25 2
5 2
55 4 15
2 15
8
16
36 2
6 2
9 10
3 10
9 11
3 11
4 30
2 30
25 6
5 6
16 10
4 10
100 2
10 2
100 3
10 3
OPERATIONS WITH RADICALS10
@iteachalgebra
Simplify each radical expression.
2 + 2 4 3 + 3 5 6 + 2 6
2 - 2 4 3 - 3 5 6 - 2 6
2 • 2 4 3 • 3 5 6 • 2 6
72 + 50 4 45 - 125 5 27 + 2 5
ANSWER KEY
2 2 5 3 7 6
0 3 3 3 6
4 = 2 4 9 = 4(3)
= 12
10 36 = 10(6)
= 60
36 2 + 25 2
6 2 + 5 2
11 2
4 9 5 + 25 5
4(3) 5 + 5 5
17 5
12 5 + 5 5
5 9 3 + 2 5
5(3) 3 + 2 5
15 3 + 2 5
CLASSIFYING SEGMENTS, RAYS, & LINES
11
@iteachalgebra
Determine the segments, rays, and lines from the diagram.
SEGMENTS RAYS LINES
A
B
CD
Determine whether each statement is true or false.
Two lines can intersect at exactly one point.
Two lines can intersect at exactly two points.
The are an infinite number of points on a line.
A ray has an arrow at one end.
A segment and a line are identical.
ANSWER KEY
𝐴𝐶 𝐵𝐶 𝐴𝐵
𝐶𝐷
true
false
true
true
false
NUMBER OF EDGES & VERTICES12
@iteachalgebra
List the number of edges and vertices for each figure.
edges:
vertices:
edges:
vertices:
edges:
vertices:
rectangular prism
square pyramid
cylinder
ANSWER KEY
12
12
8
5
none
none
ANGLE MEASUREMENTS13
@iteachalgebra
Circle the type of angle shown and the best approximate measure of the angle.
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
acute
obtuse
right
60
100
90
ANSWER KEY
TYPES OF TRIANGLES14
@iteachalgebra
Name the triangle based on its sides and angles.
Names include equilateral, isosceles, and scalene, acute, obtuse, and right.
60
60 6090
60 30
120
30 30
45
4590
40
70
70
55
8045
ANSWER KEY
acute
acute
acuteright
isosceles
isosceles
obtuse
equilateral
right
scalene
isosceles
scalene
TYPES OF QUADRILATERALS15
@iteachalgebra
Determine if the quadrilateral is a square, rectangle, rhombus, trapezoid,
isosceles trapezoid, parallelogram, or more than one of those names.
>
>
>
>
>
>
> >
ANSWER KEY
parallelogram
rectangle, square
parallelogram
trapezoid parallelogram
parallelogram
rhombus
trapezoid
PARTS OF A CIRCLE16
@iteachalgebra
Given the circle, name each part.
Find the circumference and area of each circle.
5
8
Circumference: C = 2𝜋r Area: A = 𝜋r2
Circumference: C = 𝜋d Area: A = 𝜋r2
ANSWER KEY
chord
center
radius
diameter
C = 2𝜋r
C = 2𝜋(5)
C = 10𝜋
C ~ 31.4 units
C = 𝜋d
C = 𝜋(8)
C = 8𝜋
C ~ 25.1 units
A = 𝜋r2
A = 𝜋(5)2
A = 25𝜋
A ~ 78.5 units
A = 𝜋r2
A = 𝜋(4)2
A = 16𝜋
A ~ 50.3 units
r = 4
AREA FORMULAS17
@iteachalgebra
Calculate the area of each figure.
A = lw
13.5
4
10
3
A = 1
2bh
16
9.8
A = bh
rectangle triangle
parallelogram
A = 1
2h(b1 + b2)
trapezoid
5
9
4
ANSWER KEY
A = (13.5)(4)
A = 56 units2A =
1
2(10)(3)
A = 15 units2
A = (16)(9.8)
A = 156.8 units2A =
1
2(4)(5 + 9)
A = 2(14)
A = 28 units2
VOLUME FORMULAS18
@iteachalgebra
Calculate the volume of each figure.
V = s3 V = lwh
V = r2h
cube rectangular prism
cylinder
V = 4
3r3
sphere
4
3
5
6
6
6
5
4
8.5
ANSWER KEY
V = (6)3
V = 216 units3
V = (8.5)(4)(5)
V = 170 units3
V = (3)2(4)
V = (9)(4)
V = 36 units3
V ~ 113.1 units3
V = 4
3(5)3
V = 4
3(125)
V = 500
3 units3
V ~ 523.6 units3
TRANSFORMATIONS19
@iteachalgebra
Determine the type of transformation shown in each diagram as a translation,
rotation, reflection, or dilation.
ANSWER KEY
rotation translation
reflection or rotation dilation
CONGRUENT OR SIMILAR20
@iteachalgebra
Determine whether the figures shown are congruent or similar.
ANSWER KEY
congruent
congruent
congruent similar
similar
similar