AnswersGeometry - Semester 1 PathwaysUsing Triangle Congruence Theorems

Using Triangle Congruence Theorems — Cumulative exam Answers

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Which pair of triangles can be proven congruent by SAS?

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
2
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[Figure may not be drawn to scale]

Question illustration
A
12 mm
B
24 mm
C
36 mm
D
48 mm
3

In the diagram, TRV ≅ VRW. What is the measure of SRT? mSRT = degrees

Answer not available
4

Triangle QRS is transformed as shown on the graph.

Question illustration
R
R0, 90°
R
R0, 180°
R
R0, 270°
R
R0, 360°
5

On a coordinate plane, 2 triangles are shown. The first triangle has points F (3, 2), H (4, 5), G (1, 2). The second triangle has points F prime (negative 2, 3), H prime (negative 5, 4), G prime (negative 2, 1).

Question illustration
A
Correct. He transformed the triangle according to the rule (x, y) → (–y, x).
B
Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x)
C
Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x)
D
Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)
6

Polygon LMNOP was transformed to create polygon L'M'N'O'P'.

Question illustration
A
Angle
Option A
B
Angle
Option B
C
Angle
Option C
D
Angle
Option D
7

is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .

Question illustration
A
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
B
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
C
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
D
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.
8

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
9

Figure R S T U V is reflected across a point of reflection n to form R prime S prime T prime U prime V prime. Figure R prime S prime T prime U prime V prime is rotated 270 degrees about point P to form R double-prime S double-prime T double-prime U double-prime V double-prime

Question illustration
A
a reflection across line n followed by a translation down and to the right
B
a reflection across line n followed by a 270° rotation about point P
C
a translation down followed by a 270° rotation about point P
D
a translation down followed by a reflection across line n
10

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
11

A circle is inscribed with 3 lines. Point x is at the center of the circle. A vertical line goes through point x to point z on the edge of the circle. A horizontal line goes through point x to point y on the edge of the circle. A diagonal line goes through point x to point w on the edge of the circle.

Question illustration
A
Line segment Y Z
Option A
B
Line segment W Y
Option B
C
Line segment X Z
Option C
D
Line segment W Z
Option D
12

In the diagram, mFLI is 106°, mFLG = (2x – 1)°,mGLH = (x + 17)°, and mHLI = (4x – 15)°.

Question illustration
A
15°
B
29°
C
32°
D
45°
13

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.
14

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
15

A regular decagon has 10 sides.

Question illustration
A
5
B
10
C
15
D
20
16

Which best describes the dimensions of a plane?

A
A plane has zero dimensions because it represents a location on the coordinate plane.
B
A plane has one dimension because it is made up of an infinite number of points.
C
A plane has two dimensions because it is a flat surface that has length and width but no depth.
D
A plane has three dimensions because it is made up of exactly three noncollinear points.
17

Which part of the proof does the fourth statement and reason represent?Given: AB ≅ BCBC ≅ EF Prove: EG = AB + FG

Question illustration
A
It is part of the given information.
B
It is part of the argument.
C
It is the conclusion.
D
It is an assumption.
18

Which statement describes the order of rotational symmetry for an isosceles triangle?

A
An isosceles triangle has an order 0 rotational symmetry because there is no angle at which it can be rotated onto itself.
B
An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
C
An isosceles triangle has an order 2 rotational symmetry because it has 1 pair of congruent angles.
D
An isosceles triangle has an order 3 rotational symmetry because it has 3 angles.
19

Which two undefined geometric terms always describe figures with no beginning or end?

A
a line and a plane
B
a line and a point
C
a distance and a plane
D
a distance and a point
20

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.

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