AnswersALC EAP Geometry ACumulative Exam

Cumulative Exam — Cumulative exam Answers

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21
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Point E is drawn on the graph so that line EF is parallel to line CD.

Question illustration
A
−8
B
−4
C
0
D
8
22
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Which statements regarding are true? Select three options.

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A
E F + F G greater-than E G
Option A
B
E G + F G greater-than E F
Option B
C
E G minus F G less-than E F
Option C
D
E F minus F G greater-than E G
Option D
E
E G + E F less-than F G
Option E
23

Triangles R S T and X Y T are congruent. Triangle R S T is reflected across a line and then rotated at point T to form triangle X Y T.

Question illustration
A
No, ΔRST and ΔXYT are congruent but ΔRST cannot be mapped to ΔXYT using a series rigid transformations.
B
No, ΔRST and ΔXYT are not congruent.
C
Yes, ΔRST can be reflected across the line containing RT and then rotated about T so that S is mapped to Y.
D
Yes, ΔRST can be translated so that S is mapped to Y and then rotated about S so that R is mapped to X.
24

Right triangle XYZ has a right angle at vertex Y and a hypotenuse that measures 24 cm. Angle ZXY measures 70o.What is the length of line segment XY? Round to the nearest tenth.

A
8.2 cm
B
8.7 cm
C
22.6 m
D
25.5 cm
25

The proof that ΔABC ≅ ΔCDA is shown.Given: ∥ and ∥ Prove: ΔABC ≅ ΔCDA

Question illustration
A
perpendicular bisector theorem
B
Pythagorean theorem
C
HL theorem
D
SSS congruence theorem
26

Triangle K L J is cut by line segment N O. Line segment N O goes from side L K to side L J. The length of L N is (x minus 3) inches, the length of N K is (x + 2) inches, the length of L O is (x minus 4) inches, and the length of O J is x inches.

Question illustration
A
1
B
6
C
8
D
10
27

congruencesymmetricreflexivetransitive

A
congruence
B
symmetric
C
reflexive
D
transitive
28

Which quadrilateral will always have 4-fold reflectional symmetry?

A
trapezoid
B
rhombus
C
square
D
rectangle
29

Which shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin?

Question illustration
A
On a coordinate plane, a triangle has points X (2, negative 2), Y (6, 0), Z (1, 1).
Option A
B
On a coordinate plane, a triangle has points X (2, 2), Y (6, 0), and Z (1, negative 1).
Option B
C
On a coordinate plane, a triangle has points X (negative 2, negative 2), Y (6, 0), Z (negative 1, 1).
Option C
D
On a coordinate plane, a triangle has points X (negative 2, 2), Y (negative 6, 0), Z (negative 1, negative 1).
Option D
30

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection, then rotation
B
reflection, then translation
C
rotation, then translation
D
rotation, then dilation
31

Pentagon ABCDE is dilated according to the ruleDO,3(x,y) to create the image pentagon A'B'C'D'E', which is shown on the graph.

Question illustration
A
(-1, 1)
B
(-1, 2)
C
(-9, 6)
D
(-9, 18)
32

3 lines are shown. A line with points M, H, K intersects with a line with points J, H, L at point H. Another line extends from point H to point N in between angle K, H, J. Angle M H L is (3 x + 20) degrees, angle K H N is (x + 25) degrees, and angle J H N is (x + 20) degrees.

Question illustration
A
25°
B
45°
C
50°
D
95°
33

Triangle DEF is an isosceles, so DEF DFE.

Question illustration
A
105°
B
125°
C
150°
D
165°
34

Question text not available

Question illustration
A
If a triangle is equilateral, then the triangle must also be isosceles.
B
If a triangle is isosceles, then the triangle must also be equilateral.
C
If a triangle is isosceles, then the triangle will never also be equilateral.
D
If a triangle is equilateral, then the triangle will not always be isosceles.
35

Point Q lies on the circle and has an x-coordinate of 4.

Question illustration
A
2
Option A
B
4
Option B
C
2
Option C
D
8
Option D
36

The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance between city A and city C is 51 miles.

A
an acute triangle, because 222 + 542 >512
B
an acute triangle, because 222 + 512 >542
C
an obtuse triangle, because 222 + 542 >512
D
an obtuse triangle, because 222 + 512 >542
37

Triangle RST has vertices R(2, 0), S(4, 0), and T(1, –3). The image of triangle RST after a rotation has verticesR'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°
38

The diagram represents three statements about teachers: p, q, and r.

Question illustration
A
2
B
4
C
5
D
9
39

Given: a ∥ b and ∠1 ≅ ∠3Prove: e ∥ fWe know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.Which information is missing in the paragraph proof?

Question illustration
A
∠2 ≅ ∠4
B
∠1 ≅ ∠2
C
∠2 ≅ ∠3
D
∠1 ≅ ∠4
40

On a coordinate plane, 2 triangles are shown. Triangle 1 has points at A (negative 3, 4), B (negative 2, 1), C (negative 4, 1). Triangle 2 has points at A prime (4, negative 2), B prime (3, negative 5), C prime (5, negative 5).

Question illustration
A
(x, y) → (x + 7, y + 6)
B
(x, y) → (x + 7, y – 6)
C
(x, y) → (x – 6, y + 7)
D
(x, y) → (x + 6, y + 7)

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