AnswersMathematics ITriangle Congruence

Triangle Congruence — Test Answers

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What is the perimeter of rectangle EFGH ?

A
39 units
B
2 square root of 10 plus 2 square root of 29 units
C
22 units
D
square root of 10 plus square root of 29 units
3

line segment BC is parallel to line segment AD and line segment CD is parallel to line segment BA because the ________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

A
lengths of opposite sides are equal
B
lengths of consecutive sides are not equal
C
slopes of consecutive sides are not equal
D
slopes of opposite sides are equal
4

What is the missing reason in the proof?

A
the third angle theorem
B
AAS
C
ASA
D
the reflexive property
5

What is the area of triangle LMN ?

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

In the diagram, angle cap j is congruent to angle cap m and line segment JL is congruent to line segment MR What additional information is needed to show triangle JKL is congruent to triangle MNR by SAS?

A
angle cap k is congruent to angle cap n
B
line segment JK is congruent to line segment MN
C
angle liters is congruent to angle cap r
D
line segment KL is congruent to line segment NR
9

What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem?

A
angle cap l cap o cap A is congruent to angle cap l cap m cap A
B
line segment cap l cap o is congruent to line segment cap l cap m
C
line segment cap o cap A is congruent to line segment cap m cap A
D
angle cap l cap A cap o is congruent to angle cap l cap A cap m
10

What is the total area of the three triangles?

A
12 point 5 square units
B
13 square units
C
13 point 5 square units
D
14 square units
11

Could triangle JKL be congruent to triangle XYZ ? Explain.

A
No, because the leg of one triangle is equal in length to the leg of the other triangle.
B
Yes, if XZ is equal to 10 .
C
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
D
Yes, if line segment JL is congruent to line segment XZ .
12

In triangle XYZ , m angle cap x is equal to 90 degrees and m angle cap y is equal to 30 degrees In triangle TUV , m angle cap u is equal to 30 degrees and m angle cap v is equal to 60 degrees Which is true about the two triangles?

A
triangle XYZ is congruent to triangle TUV
B
triangle XYZ is congruent to triangle VUT
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.
14

Which pair of triangles can be proven congruent by SAS?

A
Image with description 2 triangles have a common side, 2 congruent bases, and 2 congruent altitudes.
B
Image with description A triangle has no labels. A perpendicular bisector is drawn from the vertex to the opposite base and divides the base into 2 equal halves, so 2 identical triangles are formed.
C
Image with description 2 congruent triangles have a common altitude, congruent angles at the vertex, and congruent base angles at the altitude.
D
Image with description 2 triangles have congruent bases, congruent side lengths, and congruent angles that are not included between two congruent sides.
15

How does the area of triangle ABC compare to the area of parallelogram GHJK ?

A
The area of triangle ABC is 2 square units greater than the area of parallelogram GHJK .
B
The area of triangle ABC is 1 square unit greater than the area of parallelogram GHJK .
C
The area of triangle ABC is 1 square unit less than the area of parallelogram GHJK .
D
The area of triangle ABC is equal to the area of parallelogram GHJK .
16

In the diagram, SR is equal to 4 square root of 2 and QR is equal to square root of 10 What is the perimeter of parallelogram PQRS ?

A
16 square root of 2 units
B
square root of 10 units
C
8 square root of 2 plus 2 square root of 10 units
D
8 square root of 2 plus 8 units
18

How can a translation and a reflection be used to map triangle HJK to triangle LMN ?

A
Translate cap k to cap n and reflect across the line containing line segment JK .
B
Translate cap h to cap l and reflect across the line containing line segment JK .
C
Translate cap k to cap l and reflect across the line containing line segment HJ .
D
Translate cap k to cap n and reflect across the line containing line segment HJ .
19

What is the area of parallelogram RSTU ?

A
24 square units
B
21 square units
C
32 square units
D
28 square units
21

Which statement proves that triangle XYZ is an isosceles right triangle?

A
line segment XZ perpendicular to line segment XY
B
The slope of line segment XZ is 3 fourths , the slope of line segment XY is negative 4 thirds , and XZ is equal to XY is equal to 5 .
C
The slope of line segment XZ is 3 fourths , the slope of line segment XY is negative 4 thirds , and the slope of line segment ZY is equal to 7 .
D
XZ is equal to XY is equal to 5

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