Using Triangle Congruence Theorems Answers

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Let p: A student plays basketball.Let q: A student plays tennis.

Question illustration
A
4
B
8
C
32
D
36
2
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Which statements regarding the diagram of ΔEBC are true? Select three options.

A
∠BEC is an exterior angle.
B
∠DEC is an exterior angle.
C
∠ABE and ∠EBC are supplementary angles.
D
∠BCF and ∠DEC are supplementary angles.
E
∠BEC is a remote interior angle to exterior ∠BCF.
3

Let p: The shape is a rhombus.Let q: The diagonals are perpendicular.Let r: The sides are congruent.Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

A
p ∧ (q ∧ r)
B
(p ∨ q) ∨ r
C
p ↔ (q ∧ r)
D
(p ∨ q) ↔ r
4

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees.

Question illustration
A
m∠ABC = 15°
B
m∠ABC = 45°
C
m∠ABC = 60°
D
m∠ABC = 75°
5

Let p: The number is even.Let q: The number is prime.Which statement is represented by p ∧ q?

A
The number is even and prime.
B
The number is even or prime.
C
The number is even if the number is prime.
D
The number is prime if the number is even.
6

The truth table represents statements p, q, and r. pqrq ∧ r ATT T T BTTF F C T FT F DT F FF EF T T T FF T F F GF F T F HF F F F

A
E
B
F
C
G
D
H
7

2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. The top angle of the triangle is (2 x + 10) degrees. The bottom right angle of the triangle is 79 degrees. The exterior angle to the bottom left angle is (6 x + 1) degrees.

Question illustration
A
x = 2.25
B
x = 11.25
C
x = 13
D
x = 22
8

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Question illustration
A
∠JKL
B
∠MKL
C
∠KLM
D
∠LMK
9

Let p: x = 4Let q: y = −2Which represents "If x = 4, then y = −2”?

A
p ∨ q
B
p ∧ q
C
p → q
D
p ↔ q
10

Triangle X Y Z is shown.

Question illustration
A
m∠Y = 26°
B
m∠Y = 34°
C
m∠Y = 60°
D
m∠Y = 120°
11

Let p: A number is greater than 25.Let q: A number is less than 35.If p ∧ q is true, then what could the number be? Select two options.2428323640

A
24
B
28
C
32
D
36
E
40
12

Let p: x 3What is represented by p ∨ q?

A
x 3
B
x > 3 or x < −3
C
If x 3
D
x 3
13

Which biconditional statement is true?

A
A shape is a rectangle if and only if the shape has exactly four sides and four right angles.
B
A shape is a trapezoid if and only if the shape has a pair of parallel sides.
C
A shape is a triangle if and only if the shape has three sides and three acute angles.
D
A shape is a square if and only if the shape has exactly four congruent sides.
14

The diagram represents two statements: p and q.

Question illustration
A
p ∨ q
B
p → q
C
q ∧ p
D
q → p
15

Triangle R T S is sitting on a horizontal line. Line S R extends through point Q to form exterior angle T R Q. Angle R T S is (25 x) degrees. Angle T S R is (57 + x) degrees. Exterior angle T R Q is (45 x) degrees.

Question illustration
A
x = 2
B
x = 3
C
x = 33
D
x = 52
16

The diagram represents two statements: p and q.

Question illustration
A
p ∨ q
B
p → q
C
q ∧ p
D
q → p
17

Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.

Question illustration
A
m∠WXY = m∠YXZ
B
m∠WXY < m∠YZX
C
m∠WXY + m∠YXZ = 180°
D
m∠WXY + m∠XYZ = 180°
18

A triangle is shown with a line extending from the bottom left point

Question illustration
A
An exterior angle is supplementary to the adjacent interior angle.
B
An adjacent interior angle is supplementary to a remote interior angle.
C
A remote interior angle is congruent to the exterior angle.
D
An exterior angle is supplementary to a remote interior angle.
19

The diagram represents three statements about animals at the zoo: p, q, and r.

Question illustration
A
15
B
17
C
20
D
22
20

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

A
A and B
B
A, B, and C
C
B and E
D
B, C, and E

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