Understanding Proofs and Constructions Unit Test 96%

Given: mEDF = 120°; mADB = (3x)°; mBDC = (2x)° Prove: x = 24 What is the missing reason in step 3?

vertical angles are congruent

Which statement is true about the diagram?

K is the midpoint of AB.

Which pair of angles are vertical angles?

WRS and VRT

A paragraph proof

contains a table with a logical series of statements and reasons.

What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠DBC is a straight angle Prove: ∠ABC ≅ ∠ABD

definition of congruent angles

Given that BA bisects ∠DBC, which statement must be true?

m∠ABD = m∠ABC

Given that EB bisects ∠CEA, which statements must be true? Check all that apply.

m∠CEA = 90° m∠BEF = 135° ∠CEF is a straight angle. ∠AEF is a right angle.

Segment AB is congruent to segment AB. This statement shows the ______ property.

reflexive

In the diagram, what is the measure of WRS?

25°

Triangle ABC is a right triangle. What is the relationship between angles A and B?

They are complementary.

Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. Which statement is true about angles 3 and 5?

They are supplementary.

Figure JKLM is a rectangle, so mKJM = mKLM = 90° and KJC MLC. Which reason justifies the statement that KLC is complementary to KJC?

Angles that are congruent are complementary to the same angle.

In the diagram, what is mVSR?

mVSR = 80°

Line JM intersects line GK at point N. Which statements are true about the figure? Check all that apply.

MNL is complementary to KNL. Line JM intersects line GK at point N. GNM is supplementary to JNK.

Angle RST is a right angle. Angle RSU has a measure of 25°. What is the measure of angle TSU?

65°

Given that ∠CEA is a right angle and EB bisects ∠CEA, which statement must be true?

m∠CEB = 45°

In which diagram do angles 1 and 2 form a linear pair?

D

Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?

He is incorrect. Ray RO and ray RL are not opposite rays.

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

angle addition postulate

In which diagram are angles 1 and 2 vertical angles?

A

In the diagram, which angles are vertical angles? Check all that apply.

ABE and CBD ABC and EBD

Which angle is a vertical angle with EFD?

AFB

Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?

AK + BK = AC

The last step in a proof contains the

conclusion

A flowchart proof

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