Introduction to Proof Assignment and Quiz

A two-column proof

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

Given: EB bisects ∠AEC. ∠AED is a straight angle. Prove: m∠AEB = 45° Complete the paragraph proof. We are given that EB bisects ∠AEC. From the diagram, ∠CED is a right angle, which measures __° degrees. Since the measure of a straight angle is 180°, the measure of angle ______ must also be 90° by the _____. A bisector cuts the angle measure in half. m∠AEB is 45°.

90 AEC angle addition postulate

Given: ∠ABC is a right angle and ∠DEF is a right angle. Prove: All right angles are congruent by showing that ∠ABC ≅∠DEF. What are the missing reasons in the steps of the proof?

A: definition of right angle B: substitution property C: definition of congruent angles

Given: m∠ABC = m∠CBD Prove: BC bisects ∠ABD. Justify each step in the flowchart proof.

A: given B: definition of congruent C: definition of bisect

Identify the missing parts in the proof. Given: ∠ABC is a right angle. DB bisects ∠ABC. Prove: m∠CBD = 45°

A: given B: measure of angle ABC = 90 C: angle addition postulate D: 2 times the measure of angle CBD = 90

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

AK + BK = AC

Which statement is true about the diagram?

K is the midpoint of AB.

Name the three different types of proofs you saw in this lesson. Give a description of each.

One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.

Describe the main parts of a proof.

Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

Given that RT ≅ WX, which statement must be true?

RT + TW = WX + TW

Given: m∠A + m∠B = m∠B + m∠C Prove: m∠C = m∠A Write a paragraph proof to prove the statement.

We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.

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

m∠ABD = m∠ABC

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

m∠CEB = 45°

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

reflexive

Which property is shown? If m∠ABC = m∠CBD, then m∠CBD = m∠ABC

symmetric property

What is the missing justification?

transitive property

Given that ∠ABC ≅ ∠DBE, which statement must be true?

∠ABD ≅ ∠CBE

Which statement is true about the diagram?

∠BEA ≅ ∠BEC

EB bisects ∠AEC. What statements are true regarding the given statement and diagram?

∠CED is a right angle. ∠CEA is a right angle. m∠CEB = m∠BEA m∠DEB = 135°