Introduction to Proof

Question 1

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 2

measure of angle ABC = 90measure of angle ABC = 180measure of angle ABD = 90 measure of angle CBD = 180

Revolt · Accepted Answer

measure of angle ABC = 90

Question 3

Justify each step in the flowchart proof.

Revolt · Accepted Answer

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

Question 4

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 5

AEB ✔ AEC BEC BED

Revolt · Accepted Answer

✔ AEC

Question 6

✔ angle addition postulate reflexive property segment addition property symmetric property

Revolt · Accepted Answer

✔ angle addition postulate

Question 7

Given: ∠ABC is a right angle and ∠DEF is a right angle.

Revolt · Accepted Answer

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

Question 8

identity propertyreflexive property ✔ substitution propertysymmetric property

Revolt · Accepted Answer

✔ substitution property

Question 9

✔ definition of congruent angles definition of equal angles substitution property symmetric property

Revolt · Accepted Answer

✔ 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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