Answers NY-Geometry Term 1 HillcrestWriting Linear Equations

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Which points lie on the line that passes through point P and is parallel to the given line? Select three options.

(–4, 2)

(–1, 3)

(–2, 2)

(4, 2)

(–5, –1)

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Consider the two planes.

line a.

line b.

line d.

plane Q.

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

Option

Consider the diagram.

They lie in different planes and will never intersect.

They lie in the same plane but will never intersect.

They lie in different planes but will intersect if a plane is drawn to contain both lines.

They lie in different planes and will be parallel if a plane is drawn to contain both lines.

Two parallel lines are crossed by a transversal.

m = 68

m = 78

m = 102

m = 112

Two parallel lines are crossed by a transversal.

g = 75

g = 80

g = 100

g = 105

Two parallel lines are crossed by a transversal.

m = 68

m = 78

m = 102

m = 112

In the diagram, the length of segment TR can be represented by 5x – 4.

3 units

11 units

13 units

15 units

What value is a counterexample for the conditional statement shown?If a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1, the number itself, and the square root of the number.

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

x + 2y = 4

x + 2y = 8

2x + y = 4

2x + y = 8

Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.

They are complementary.

They are supplementary.

They are congruent.

They are obtuse.

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?

vertical angles theorem

alternate exterior angles theorem

converse corresponding angles theorem

converse alternate interior angles theorem

In the diagram, which angles form a linear pair? Select three options.

RST and RSV

RST and TSU

RST and VSU

TSU and USV

TSU and RSV

Lines c and d are intersected by line p. At the intersection of lines c and p, the bottom left angle is (3 x + 45) degrees. At the intersection of lines d and p, the uppercase left angle is 81 degrees.

Given: AB = BCProve: B is the midpoint of AC.

two-column proof

one-paragraph proof

flowchart proof

two-paragraph proof

Which diagram shows lines that must be parallel lines cut by a transversal?

2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 91 degrees. At the intersection with the second line, the bottom right angle is 91 degrees.

2 horizontal lines are intersected by another line. At the intersection with the first line, uppercase right angle is 91 degrees and the bottom left angle is 91 degrees.

2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 89 degrees and the bottom right angle is 91 degrees.

2 horizontal lines are intersected by another line. At the intersection with the first line, the bottom right angle is 91 degrees. At the intersection with the second line, the top right angle is 89 degrees.

Inductive and deductive reasoning differ in which way?

Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true.

Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.

Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true.

Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negative 2) and (0, negative 4).

They are parallel because their slopes are equal.

They are parallel because their slopes are negative reciprocals.

They are not parallel because their slopes are not equal.

They are not parallel because their slopes are negative reciprocals.

The converse of a conditional statement is "If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.”What is the inverse of the original conditional statement?

If a figure is a polygon, then the sum of the exterior angles is 360°.

If the sum of the exterior angles of a figure is not 360°, then the figure is not a polygon.

If the sum of the exterior angles of a figure is 360°, then the figure is not a polygon.

If a figure is not a polygon, then the sum of the exterior angles is not 360°.

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).

They are parallel because their slopes are equal.

They are parallel because their slopes are negative reciprocals.

They are not parallel because their slopes are not equal.

They are not parallel because their slopes are negative reciprocals.

Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?

45°

60°

120°

135°

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

y − 1 = −2(x − 4)

y – 1 = (x – 4)

y – 1 = (x – 4)

y − 1 = 2(x − 4)

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

6 units

8 units

12 units

16 units

Let p: The whole number has one digit.Let q: The whole number is less than 10.Which represents "The whole number has one digit if and only if the whole number is less than 10”?

p ∨ q

p ∧ q

p → q

p ↔ q

On a coordinate plane, a line goes through (1, negative 1) and (4, 2). A point is at (2, 5).

y + 5 = x + 2

y − 2 = x − 5

y − 5 = −(x − 2)

y + 2 = −(x + 5)

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R is at (4, 2).

(–6, 10)

(–4, –8)

(0, –1)

(2, 4)

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

r → (p ∧ q)

r → (p ∨ q)

(q ∧ r) → p

(q ∨ r) → p

Two parallel lines, e and f, are crossed by two transversals.

m15 = 77°

m15 = 83°

m15 = 93°

m15 = 97°

Lines e and f are intersected by line a. At the intersection of lines a and e, the bottom right angle is 72 degrees. At the intersection of lines a and f, the uppercase right angle is 108 degrees.

alternate interior angles theorem

same side interior angles theorem

converse of the alternate interior angles theorem

converse of the same side interior angles theorem

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

y = –x + 5

y = –x + 3

y = 3x + 2

y = 3x − 5

Given: and g is a transversalProve:

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

Given: and g is a transversalProve:

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

Which is logically equivalent to the converse of a conditional statement?

the original conditional statement

the inverse of the original conditional statement

the contrapositive of the original conditional statement

the converse of the converse statement

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