AnswersMathematics for College Liberal Arts Sem 2 1207350 BCPS 2026-27Area of Triangles and Parallelograms

Area of Triangles and Parallelograms — Unit test Answers

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Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
2
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On a coordinate plane, triangle X Y Z is shown. Point X is at (1, 3), point Y is at (4, negative 1), and point Z is at (5, 6).

Question illustration
A
XZ is not perpendicular to XY
B
XZXY
Option B
C
The slope of XZ is , the slope of XY is , and XZ = XY = 5.
Option C
D
The slope of XZ is , the slope of XY is , and the slope of ZY = 7.
Option D
3

Triangles J K L and M N R are shown.

Question illustration
A
KL ≅ NR
B
∠L ≅ ∠R
C
∠K ≅ ∠N
D
JK ≅ MN
4

Which pair of triangles can be proven congruent by SAS?

A
2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.
Option A
B
2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.
Option B
C
2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.
Option C
D
2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.
Option D
5

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

A
ΔXYZ ≅ ΔTUV
B
ΔXYZ ≅ ΔVUT
C
No congruency statement can be made because only two angles in each triangle are known.
D
No congruency statement can be made because the side lengths are unknown.
6

The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

Question illustration
A
definition of perpendicular bisector
B
definition of congruence
C
reflexive property
D
substitution property
7

On a coordinate plane, triangle L M N has points (negative 1, 2), (negative 1, negative 4), and (3, negative 4).

Question illustration
A
12 square units
B
14 square units
C
15 square units
D
24 square units
8

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

Question illustration
A
the reflexive property
B
ASA
C
AAS
D
the third angle theorem
9

Quadrilateral L M N O is reflected over a line to form quadrilateral C D A B.

Question illustration
A
AB
B
AD
C
CB
D
DC
10

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

Question illustration
A
a reflection across the line containing AB
B
a rotation about point B
C
a reflection across the line containing CB
D
a rotation about point C
11

On a coordinate plane, parallelogram R S T U has points (negative 3, 2), (4, negative 1), (4, negative 4), and (negative 3, negative 1).

Question illustration
A
21 square units
B
24 square units
C
28 square units
D
32 square units
12

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2).

Question illustration
A
units
Option A
B
+ units
Option B
C
units
Option C
D
+ 8 units
Option D
13

On a coordinate plane, triangle A B C and parallelogram G H J K are shown. Triangle A B C has points (2, 0), (1, negative 6), (negative 2, negative 4). Parallelogram G H J K has points (0, 0), (1, 2), (negative 2, 4), and (negative 3, 2).

Question illustration
A
The area of △ABC is 2 square units greater than the area of parallelogram GHJK.
B
The area of △ABC is 1 square unit greater than the area of parallelogram GHJK.
C
The area of △ABC is equal to the area of parallelogram GHJK.
D
The area of △ABC is 1 square unit less than the area of parallelogram GHJK.
14

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection only
B
rotation only
C
translation, then reflection
D
translation, then rotation
15

Complete the proof to show that ABCD is a parallelogram. The slope of is The slope of is The slope of is The slope of is

Question illustration
A
lengths of consecutive sides are not equal
B
slopes of opposite sides are equal
C
lengths of opposite sides are equal
D
slopes of consecutive sides are not equal
16

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Question illustration
A
Yes, if JL ≅ XZ.
B
Yes, if XZ = 10.
C
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
D
No, because the leg of one triangle is equal in length to the leg of the other triangle.
17

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

Question illustration
A
LO ≅ LM
B
OA ≅ MA
C
LOA ≅ LMA
Option C
D
LAO ≅ LAM
Option D
18

Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.

Question illustration
A
No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.
B
No, ΔQRS and ΔABC are not congruent.
C
Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.
D
Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.
19

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Question illustration
A
Yes, they are congruent by either ASA or AAS.
B
Yes, they are both right triangles.
C
No, M is not congruent to NLQ.
Option C
D
No, there are no congruent sides.
20

Quadrilateral ABCD is translated down and left to form quadrilateral OLMN.

Question illustration
A
5 units
B
6 units
C
8 units
D
10 units

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