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GSE Geometry Unit 1 Study Guide

Total questions: 46

Worksheet time: 2hrs 18mins

Name
Class
Date
1.

As shown in the diagram below, when right
triangle DAB is reflected over the x-axis, its image
is triangle DCB. 

Which statement justifies why 

 AB‾≅BC‾?\overline{AB}≅\overline{BC}?  

a)

Distance is preserved under reflection.

b)

Orientation is preserved under reflection.

c)

Points on the line of reflection remain unchanged.

d)

Right angles remain congruent under reflection.

2.

The image of ABC after a rotation of 90º

clockwise about the origin is DEF, as shown
below.

a)

 BC‾≅DE‾\overline{BC}\cong\overline{DE}  

b)

 AB‾≅DF‾\overline{AB}\cong\overline{DF}  

c)

 ∠C≅∠E\angle C\cong\angle E  

d)

 ∠A≅∠D\angle A\cong\angle D  

3.

After a reflection over the y-axis, the image of ABC is A′B′C′. Which statement is not true?



Right triangle ABC is shown in the graph below.

a)

 BC ‾≅B′C′‾\overline{BC\ }\cong\overline{B'C'}  

b)

 A′B′‾ ⊥ B′C′‾\overline{A'B'}\ \perp\ \overline{B'C'}  

c)

AB = A'B'

d)

 AC‾∥ A′C′‾\overline{AC}\parallel\ \overline{A'C'}  

4.

In the diagram below, ABC with sides 13, 15,

and 16, is mapped onto DEF after a clockwise

rotation of 90° about point P.


If DE = 2x − 1, what is the value of x?

a)

7

b)

7.5

c)

8

d)

8.5

5.
Write a rule for the translation.
a)
 (x -1, y  + 2)
b)
 (x -2, y  + 1)
c)
 (x +2, y  - 1)
d)
(x +1, y  -  2)
6.

Write a description of the rule (x,y) --> (x +10, y+8)

a)

translation 10 units to the right and 8 units up

b)

translation 10 units to the left and 8 units down

c)

translation 10 units to the right and 8 units down

d)

translation 10 units to the left and 8 units up

7.

A triangle has vertices at A (1, 3), B (4, 2), and C (3, 8). Which transformation would produce an image with

vertices A'(3, - 1), B'(2, - 4), C'(8, - 3)?

a)

a reflection over the x-axis

b)

a reflection over the y-axis

c)

a rotation 90° clockwise

d)

a rotation 90° counterclockwise

8.

A triangle has vertices at F (-7, 3), G (2, 6), and H (3, 5). What are the coordinates of each vertex if the triangle is

reflected over the x axis?

a)

F'(-7, - 3), G'(2, - 6), H'(3, - 5)

b)

F'(7, - 3), G'(-2, - 6), H '(-3, - 5)

c)

F(7, 3), G(-2, 6), H'(-3, 5)

d)

F'(-7, 3), G'(-2, 6), H'(-3, - 5)

9.

A triangle has vertices at A(-3, - 1), B(-6, - 5), C(-1, - 4). Which transformation would produce an image with

vertices A'(3, - 1), B'(6, - 5), C'(1, - 4)?

a)

a reflection over the x-axis

b)

a reflection over the y-axis

c)

a rotation 90° clockwise

d)

a rotation 90° counterclockwise

10.

Determine which rotations will map this figure to itself.


i. 45°

ii. 60°

iii. 120°

iv. 180°

a)

iii only

b)

ii and iii

c)

ii, iii, and iv

d)

iii and iv

11.

Determine the angle of rotation for A to map onto A’.

a)

45

b)

135

c)

90

d)

180

12.

1. How many lines of symmetry does this shape have?

a)

1

b)

2

c)

3

d)

4

13.

2. How many lines of symmetry does the picture have?

a)

1

b)

2

c)

4

d)

0

14.

3. What is the order of rotation in the recycling symbol?

a)

0

b)

1

c)

2

d)

3

e)

infinite

15.

4. What is the order of rotation of this shape?

a)

4

b)

5

c)

6

d)

7

e)

8

16.

7. What is the angle of rotational symmetry when the order is 10?

a)

18°

b)

36°

c)

45°

d)

72°

17.

9. How many shapes have MORE THAN ONE line of symmetry?

a)

2

b)

4

c)

6

d)

8

18.

Which of the statement is TRUE for this image?

a)

Order of Rotation is 3 and Line of Reflection is 3

b)

Order of Rotation is 6 and Line of Reflection is 6

c)

Order of Rotation is 3 and Line of Reflection is 6

d)

Order of Rotation is 6 and Line of Reflection is 3

19.

A figure has _______ symmetry when a line (or lines) divide the shape into two equal parts.

a)

Line

b)

Rotational

c)

Point

20.
When copying line segment AB using a straight edge and a compass, the compass should be used to:
a)
Draw an arc above point A
b)
Measure the length of segment AB
c)
Draw an arc between point A and point B
d)
Measure half the length of line segment AB
21.
Suppose we wish to construct a perpendicular bisector of line segment EF. We can correctly begin by placing the compass point on E and marking off the distance to which point?
a)
A
b)
B
c)
C
d)
D
22.
To inscribe a hexagon inside a circle, which length should you set your compass to?
a)
The radius
b)
The diameter
c)
Half of the radius
d)
It depends on the size of the circle
23.
Suppose we wish to construct angle EFG congruent to angle DBC using a compass and straightedge. Which step would be correct to do first?
a)
Place the compass point at B
b)
Place the compass point at C
c)
Place the straightedge along A and C
d)
Place the straightedge along C and D
24.
When bisecting an angle, the straightedge should be used to:
a)
Mark the point M
b)
Measure the angle AOB
c)
Copy the angle with an arc
d)
Connect point M and vertex O
25.
To inscribe a square inside a circle, first you must draw a diameter anywhere across the circle. What should your next step be?
a)
Construct a perpendicular bisector
b)
Draw a second diameter to the circle
c)
Construct a line tangent to the circle
d)
Set your compass the length of the radius.
26.
What geometric construction is shown in the diagram below?
a)
an angle bisector
b)
a line parallel to a given line
c)
an angle congruent to a given angle
d)
a perpendicular bisector of a segment
27.
Given: angle A
What is the first step in constructing the angle bisector of angle A?
a)
Draw ray AD
b)
Draw a line segment connecting points B and C.
c)
From points B and C, draw equal arcs that intersect at D.
d)
From point A, draw an arc that intersects the sides of theangle at points B and C.
28.
Based on the construction, which statement must be true?
a)
A
b)
B
c)
C
d)
D
29.
Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing?
a)
a line through P parallel to line l
b)
a line through P intersecting line l
c)
a line through P congruent to line l
d)
a line through P perpendicular to line l
30.
What does CPCTC stand for?
a)
Congruent parts of congruent triangles are congruent
b)
Corresponding parts of congruent triangles are congruent
c)
Corresponding parts of corresponding triangles are corresponding
d)
Corresponding parts of congruent triangles are Canadian.
31.
What does SAS stand for?
a)
Side-Angle-Side
b)
Super-Awesome-Side
c)
Side-Angle-Supersized
d)
Sensationally Awesome Superman
32.
What congruency postulate proves the triangles congruency?
a)
SAS
b)
ASA
c)
SSS
d)
HL
33.
What postulate would prove triangle ∆NYQ is congruent to ∆PYQ?
a)
ASA
b)
SAS
c)
SSS
d)
HL
34.
What postulate proves these triangles congruent?
a)
HL
b)
SSS
c)
SAS
d)
ASA
35.
What postulate proves these triangles congruent?
a)
SAS
b)
HL
c)
AAS
d)
ASA
36.
Complete the congruence statement.
a)
CRP
b)
PCR
c)
RPC
d)
PRC
37.
∆ABC≅∆XYZ
which is true?
a)
AB≅XY
b)
AB≅YX
c)
AB≅XZ
d)
BC≅CB
38.
 ∠A = ≅
a)
∠M
b)
∠N
c)
∠L
39.
If ∆PIG ≅ ∆COW, WO≅?
a)
GI
b)
PI
c)
PG
40.
Name the corresponding angle or side.
a)
A
b)
B
c)
C
d)
D
41.
Which is a correct congruence statement.
a)
A
b)
B
c)
C
d)
D
42.
These triangles are congruent. If ∠E is 45o and ∠B is 55o what is the measure of ∠C?
a)
45o
b)
55o
c)
80o
d)
100o
43.
What is the measure of <C?
a)
5º
b)
25º
c)
100º
d)
125º
44.
Remember order matters. Which of the following is true?
a)
∆FGH ≅ ∆VHW
b)
∆HFG ≅ ∆HWV
c)
∆HGF ≅ ∆VHW
d)
∆FGH ≅ ∆VWH
45.
What additional information is required to prove the two triangles are congruent by ASA?
a)
A)
b)
B)
c)
C)
d)
D)
46.
What additional information is required to prove the two triangles are congruent by HL?
a)
A)
b)
B)
c)
C)
d)
D)

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