Understanding Proofs and Constructions Unit Test

Questions and Answers

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 the measure of WRS?

25°

Which statements are true about the figure? (Select all that apply)

MNL is complementary to KNL. (correct)

Line JM intersects line GK at point N. (correct)

GNM is supplementary to JNK. (correct)

None of the above.

What does a flowchart proof use?

A visual representation of the logical flow of steps needed to reach a conclusion. Signup and view all the answers

Given that EB bisects ∠CEA, which statements must be true? (Select all that apply)

m∠CEA = 90° Signup and view all the answers

In the diagram, what is mVSR?

mVSR = 80° Signup and view all the answers

The last step in a proof contains the _____

conclusion Signup and view all the answers

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

65° Signup and view all the answers

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

Angle addition postulate Signup and view all the answers

Which statement is true about angles 1 and 5 when two parallel lines are intersected by a third line?

They are supplementary. Signup and view all the answers

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

D Signup and view all the answers

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 Signup and view all the answers

In which diagram are angles 1 and 2 vertical angles?

A Signup and view all the answers

In the diagram, which angles are vertical angles? (Select all that apply)

ABE and CBD Signup and view all the answers

Which statement is true about the diagram?

K is the midpoint of AB. Signup and view all the answers

Which pair of angles are vertical angles?

WRS and VRT Signup and view all the answers

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

m∠ABD = m∠ABC Signup and view all the answers

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

AK + BK = AC Signup and view all the answers

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

reflexive Signup and view all the answers

Which angle is a vertical angle with EFD?

AFB Signup and view all the answers

What does a paragraph proof contain?

A table with a logical series of statements and reasons. Signup and view all the answers

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

Vertical angles are congruent Signup and view all the answers

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

m∠CEB = 45° Signup and view all the answers

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. Signup and view all the answers

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

They are complementary. Signup and view all the answers

Study Notes

Geometry Concepts and Proofs

A rectangle has right angles; therefore, angles that are congruent are complementary to the same angle.
Measure of angle WRS is 25° indicating the specific angle properties in geometric diagrams.

Diagram Analysis

Line JM intersects line GK at point N, leading to complementary and supplementary angle relationships.
Statements include: MNL is complementary to KNL and GNM is supplementary to JNK.

Proof Types

A flowchart proof visually represents logical steps to reach a conclusion.
A paragraph proof consists of a written series of statements and reasons demonstrating a logical argument.

Angle Relationships

If angle RST is right and angle RSU measures 25°, then angle TSU measures 65°.
If EB bisects angle CEA, then m∠CEA equals 90°, with implications for related angle measures.

Angle Measurements and Postulates

Angle addition postulate applies when deriving x value in angle relationships, such as in triangle TRV with given angle measures.
Vertical angles are formed when two lines intersect, ensuring congruency.

Midpoint and Segment Properties

If D is the midpoint of AB and K is the midpoint of BC, the sum of segments AK and BK equals the whole segment AC.
Reflexive property states that a segment is congruent to itself, as shown with segment AB.

Specific Angle Relationships

If angles are vertical (e.g., ABE and CBD), they are congruent.
The definition of congruent angles is applicable when comparing right angles and straight angles.

Misconceptions and Clarifications

Misstatements about angles like linear pairs can arise; it is critical to confirm ray orientation (e.g., ORP and LRP).

Triangle Properties

In a right triangle, the two non-right angles are complementary, reinforcing the fundamental principles of triangle properties.

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