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3 lines are shown. One line has points B, A, and E. Another line with points C, A, F intersects that line at point A. Another line comes out of point A and contains point D.

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line XY

line XZ

line WX

line WZ

Which statements are true about the figure? Select two options.

GNJ is complementary to JNK.

MNL is complementary to KNL.

MNG is complementary to GNJ.

KNJ is supplementary to MNL.

GNM is supplementary to JNK.

Given:p: Angles XYZ and RST are vertical angles.q: Angles XYZ and RST are congruent.Which statement is logically equivalent to p → q?

If angles XYZ and RST are congruent, then they are vertical angles.

If angles XYZ and RST are not vertical angles, then they are not congruent.

If angles XYZ and RST are not congruent, then they are not vertical angles.

If angles XYZ and RST are vertical angles, then they are not congruent.

Figure JKLM is a rectangle, so mKJM = mKLM = 90° and KJC MLC.

Angles that are congruent are complementary to the same angle.

Angles that are congruent are supplementary to the same angle.

All angles in a rectangle are right angles.

Complementary angles are always also congruent.

Given: mTRV = 60° mTRS = (4x)°Prove: x = 30What is the missing reason in step 3?

substitution property of equality

angle addition postulate

subtraction property of equality

addition property of equality

A flowchart proof

contains a set of sentences explaining the steps needed to reach a conclusion.

uses inductive reasoning to prove a statement.

uses a visual representation of the logical flow of steps needed to reach a conclusion.

contains a table with a logical series of statements and reasons that reach a conclusion.

Given that bisects ∠CEA, which statements must be true? Select three options.

m∠CEA = 90°

m∠CEF = m∠CEA + m∠BEF

m∠CEB = 2(m∠CEA)

∠CEF is a straight angle.

∠AEF is a right angle.

If an original conditional statement is represented using p → q, which represents the converse?

~p → ~q

~q → ~p

q → p

p → q

If the statement is rewritten as a conditional statement in if-then form, which best describes the hypothesis?Two lines in a plane intersect at a point.

two lines in a plane intersect

two lines intersect at a point

a point exists

points are in a plane

The diagram shows several planes, lines, and points.

Line h intersects line f at two points, A and B.

Line h is the intersection of planes R and T.

Line h intersects plane P at point C.

Line h has points on planes R, P, and T.

Point G lies between points F and H on .

When using a counterexample to prove a conditional statement false, which must be true about the counterexample?

There must be infinite counterexamples.

The counterexample must satisfy the hypothesis of the conditional statement.

There must be at least one example under which the conditional statement is true.

The counterexample must satisfy the conclusion of the conditional statement.

Line segment AB measures 18 units. What is d, the distance between tick marks on the number line?

1 unit

2 units

3 units

9 units

A horizontal line contains points A, C, B. 2 lines extend from point C. A line extends to point E and another line extends to point D. An arc represents angle A C D.

mECD = mECB

mACE = mACD

ACE DCB

ECD ACD

Which undefined geometric term is described as an infinite set of points that has length but not width?

distance

line

plane

sphere

What is the distance between points A and B?

units

5 units

6 units

3 lines are shown. A line with points T, R, W intersects a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is (5 x) degrees and angle T, R, S is (25 x + 30) degrees.