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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Which pair of triangles can be proven congruent by the HL theorem?

A
2 right triangles have congruent hypotenuses.
Option A
B
2 triangles have one congruent angle and 2 congruent sides.
Option B
C
2 right triangles have congruent hypotenuses and another congruent side.
Option C
D
2 triangles have 3 congruent sides.
Option D
2
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On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, negative 1), (2, negative 1), and (negative 1, negative 5). Triangle R S T has points (1, 1), (1, 5), and (4, 1).

Question illustration
A
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.
B
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down.
C
The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C.
D
The figures are not congruent. Point R does not correspond with point A.
3

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws.

Question illustration
A
2 (18 + 4)
B
(18 + 4)
Option B
C
(18 + 4)
D
(18 - 4)
4

How can ΔABC be mapped to ΔXYZ?

Question illustration
A
vertex B to vertex Z
B
vertex B to vertex Y
C
vertex A to vertex Z
D
vertex A to vertex Y
5

On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2).

Question illustration
A
The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
B
The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2.
C
The area of parallelogram 1 is equal to the area of parallelogram 2.
D
The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
6

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Question illustration
A
Yes, they are congruent by SAS.
B
Yes, they are both right triangles.
C
No, the triangles share side XZ.
D
No, there is only one set of congruent sides.
7

Triangle ABC is rotated 45° about point X, resulting in triangle EFD.

Question illustration
A
3.3 cm
B
3.6 cm
C
4.2 cm
D
4.5 cm
8

Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

Question illustration
A
FGH ≅ KGJ because vertical angles are congruent.
Option A
B
JKG ≅ HFG because vertical angles are congruent.
Option B
C
FHG ≅ JKG because right angles are congruent.
Option C
D
HFG ≅ KJG because alternate interior angles are congruent.
Option D
9

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, 1), (negative 4, 1) and (negative 1, 5). Triangle L M N has points (1, negative 1), (1, negative 4), and (5, negative 1).

Question illustration
A
The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
B
The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
C
The figures are not congruent because point B corresponds with point N and point C corresponds with point M.
D
The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.
10

Which pair of triangles can be proven congruent by SAS?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

Question illustration
A
a rotation about point A
B
a reflection across the line containing CB
C
a reflection across the line containing BA
D
a rotation about point B
12

Galina is finding the area of triangle RST. To do so, she follows the steps in the table.Step 1Draw a rectangle around triangle RST.Step 2Find the area of the rectangle.Step 3Find the area of the three right triangles created by the sides of the rectangle and the intersection with each vertex of the triangle.Step 4Subtract the area of the right triangles from the area of the rectangle.

A
2 units by 4 units
B
3 units by 4 units
C
3 units by 5 units
D
4 units by 5 units
13

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Question illustration
A
A ≅ Q because of the third angle theorem.
Option A
B
AB ≅ QN because they are both opposite a right angle.
C
BC ≅ NM because it is given.
D
C ≅ M because right angles are congruent.
Option D
14

On a coordinate plane, triangle R S T has points (negative 3, 2), (3, 2), and (negative 1, 1). An altitude is drawn from point T to point U at (negative 1, 2).

Question illustration
A
6 square units
B
9 square units
C
12 square units
D
18 square units
15

On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (0, negative 1), point W is at (4, 0), point Y is at (3, negative 2), and point Z is at (negative 1, negative 3).

Question illustration
A
+ units
Option A
B
+ units
Option B
C
16 units
D
22 units

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