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

Revolt · Accepted Answer

✔ definition of congruent

Question 3

definition of congruent ✔ definition of bisect given reflexive property

Revolt · Accepted Answer

✔ definition of bisect

Question 4

angle ABC = 90 angle ABD = 90 2 times the measure of angle ABC = 90 ✔ 2 times the measure of angle CBD = 90

Revolt · Accepted Answer

✔ 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; A:: given; B:: definition of congruent; C:: 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.

Revolt · Accepted Answer

✔ 90; 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: 90; 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: AEC; 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: angle addition postulate

Question 9

✔ definition of right angledefinition of congruentdefinition of equaldefinition of 90 degrees

Revolt · Accepted Answer

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

Question 10

division definition of bisects definition of right angle ✔ given

Revolt · Accepted Answer

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

Introduction to Proof Answers

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