Lesson 1.4: Introduction to Proof

Question 1

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

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symmetric property

Question 2

Question 2

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measure of angle ABC = 90

Question 3

Justify each step in the flowchart proof.

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

Question 4

✔ definition of congruent definition of bisect given reflexive property

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✔ definition of congruent

Question 5

definition of congruent ✔ definition of bisect given reflexive property

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✔ definition of bisect

Question 6

Complete the paragraph proof.

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✔ 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 7

AEB ✔ AEC BEC BED

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✔ AEC

Question 8

✔ angle addition postulate reflexive property segment addition property symmetric property

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✔ angle addition postulate

Question 9

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

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

Question 10

identity propertyreflexive property ✔ substitution propertysymmetric property

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✔ substitution property

Lesson 1.4: Introduction to Proof Answers

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