AnswersGeometry AUsing Triangle Congruence Theorems

Using Triangle Congruence Theorems — Cumulative exam Answers

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21
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Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown.

Question illustration
A
He should find the midpoint of each edge of the table.
B
He should bisect each of the angles at the vertices of the triangular table top.
C
He should draw perpendicular lines through any point along the edges of the table.
D
He should draw perpendicular line segments from each corner to the opposite edge of the table.
22
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Given: and g is a transversalProve:

Question illustration
A
corresponding angles theorem
B
alternate interior angles theorem
C
vertical angles theorem
D
alternate exterior angles theorem
23

The truth table represents statements p, q, and r. pqr AT T T BT T F CT F T DT F F EF T T FF T F GF F T HF F F

A
r → (p ∧ q)
B
r → (p ∨ q)
C
(q ∧ r) → p
D
(q ∨ r) → p
24

Consider the diagram.

Question illustration
A
They lie in different planes and will never intersect.
B
They lie in the same plane but will never intersect.
C
They lie in different planes but will intersect if a plane is drawn to contain both lines.
D
They lie in different planes and will be parallel if a plane is drawn to contain both lines.
25

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.
26

Use the ruler to measure the length of to the nearest centimeter. The length of is centimeters.

Answer not available
27

In the diagram, DC is 10 units and BC is 6 units.

Question illustration
A
6 units
B
8 units
C
12 units
D
16 units
28

On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4).

Question illustration
A
y = –x + 5
Option A
B
y = –x + 3
Option B
C
y = 3x + 2
D
y = 3x − 5
29

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°
30

On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
31

Which rules could describe the rotation? Select two options.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
(x, y) → (–y, x)
E
(x, y) → (y, –x)
32

Given: g ∥ h and ∠2 ≅ ∠3Prove: e ∥ f Statements Reasons1.g || h1.given2.∠1 ≅ ∠22.corresponding angles theorm3.∠2 ≅ ∠33.given4.∠1 ≅ ∠34.transitive property5.e || f5.?What is the missing reason in the proof?

Question illustration
A
vertical angles theorem
B
alternate exterior angles theorem
C
converse corresponding angles theorem
D
converse alternate interior angles theorem
33

A transformation of ΔDEF results in ΔD'E'F'.

Question illustration
A
The transformation is a dilation.
B
The transformation is a reflection.
C
The transformation is a rotation.
D
The transformation is a translation.
34

Two lines extend from point S to create a right angle. The vertical line extends from point S through point R. The horizontal line extends right from point S through point T. A third line extends right and up from point S through point U.

Question illustration
A
TSR
Option A
B
TSU
Option B
C
USR
Option C
D
UTS
Option D
35

Inductive and deductive reasoning differ in which way?

A
Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true.
B
Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.
C
Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true.
D
Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
36

In the triangles, HG = MP and GK = PN.

Question illustration
A
mG > mP
Option A
B
mP > mG
Option B
C
HK = MN
D
HG = PN
37

Which defines a line segment?

A
two rays with a common endpoint
B
a piece of a line with two endpoints
C
a piece of a line with one endpoint
D
all points equidistant from a given point
38

Let p: A shape is a triangle.Let q: A shape has four sides.Which is true if the shape is a rectangle?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
39

Triangle DEF was tranformed to create triangle D'E'F'. Complete the statement about the transformation.

Question illustration
A
point D.
B
point E'.
C
point F.
D
point E.
40

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

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