Introduction to Proof

Question 1

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

Revolt · Accepted Answer

symmetric property

Question 2

✔ definition of congruent definition of bisect given reflexive property

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definition of congruent

Question 3

definition of congruent ✔ definition of bisect given reflexive property

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definition of bisect

Question 4

Question 4

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2 times the measure of angle CBD = 90

Question 5

What statements are true regarding the given statement and diagram?

Revolt · Accepted Answer

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

Question 6

definition of congruent definition of bisect ✔ given reflexive property

Revolt · Accepted Answer

given; Selection 1: given; Selection 2: definition of congruent; Selection 3: definition of bisect

Question 7

Describe the main parts of a proof.

Revolt · Accepted Answer

A mathematical proof typically consists of several main parts: the 'Given' statement, which provides the known information; the 'Prove' statement, which describes the conclusion to be reached; a diagram to visually represent the problem; and a series of logical steps composed of 'Statements' and 'Reasons'. Each statement must be supported by a reason, such as a definition, postulate, property, or previously proven theorem.

Question 8

Complete the paragraph proof. We are given that 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°.

Revolt · Accepted Answer

Selection 1: 90; Selection 2: AEC; Selection 3: angle addition postulate

Question 9

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: B: C:

Revolt · Accepted Answer

definition of right angle; Selection 1: definition of right angle; Selection 2: substitution property; Selection 3: definition of congruent angles

Question 10

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

Revolt · Accepted Answer

given; Selection 1: given; Selection 2: measure of angle ABC = 90; Selection 3: angle addition postulate; Selection 4: 2 times the measure of angle CBD = 90

Introduction to Proof Answers

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