AnswersBISD TX-Geometry A-CRTriangle Congruence: SAS

Triangle Congruence: SAS — Unit test Answers

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The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

2
27°
3
36°
5
54°
7
72°
2
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Consider the diagram.

Question illustration
S
SSS.
A
ASA.
S
SAS.
H
HL.
3

A line extends from a side of a triangle.

Question illustration
A
a remote interior angle
B
an adjacent interior angle
C
an exterior angle
D
a complementary angle
4

Which type of triangle will always have a perpendicular bisector that is also an angle bisector?

A
right
B
scalene
C
obtuse
D
equilateral
5

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

A
x – 1 < n < 3x + 5
B
n = 3x + 5
C
n = x – 1
D
3x + 5 < n < x – 1
6

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.
7

Triangle B C D is shown. Line D B extends through point A to form exterior angle A B C. Angle B D C is 67 degrees and Angle C D B is 60 degrees.

Question illustration
A
m∠ABC = 60°
B
m∠ABC = 67°
C
m∠ABC = 120°
D
m∠ABC = 127°
8

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
9

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

Question illustration
A
perpendicular bisector theorem
B
converse of the perpendicular bisector theorem
C
Pythagorean theorem
D
SSS congruence theorem
10

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.
11

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.
12

Triangle ABC has the angle measures shown.

Question illustration
A
Measure of angle A = 20 degrees
Option A
B
Measure of angle B = 60 degrees
Option B
C
are complementary
Option C
D
Measure of angle A + measure of angle C = 120 degrees
Option D
13

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
14

Which diagram shows possible angle measures of a triangle?

Question illustration
A
A triangle has angle lengths 35 degrees, 115 degrees, and 25 degrees.
Option A
B
A triangle has angle lengths 32 degrees, 115 degrees, and 33 degrees.
Option B
C
A triangle has angle lengths 35 degrees, 120 degrees, and 35 degrees.
Option C
D
a triangle has angle lengths 30 degrees, 120 degrees, and 20 degrees.
Option D
15

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side at point M.What is the length of ?

Question illustration
A
16 mm
B
24 mm
C
32 mm
D
48 mm
16

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Question illustration
A
Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.
B
Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.
C
Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.
D
Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.
17

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.

Question illustration
A
h = 1.5
B
h = 9
C
h = 10
D
h = 13.5
18

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

Question illustration
A
Yes, but only if AB ≅ DC.
B
Yes, but only if BC ≅ DC.
C
No, because AB is not congruent to AC.
D
No, because AB ≅ DA.
19

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
20

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation

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