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Simple Geometric Proofs

Authored by Anthony Clark

Mathematics

10th Grade

CCSS covered

Used 7+ times

Simple Geometric Proofs
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12 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
Step 2: m∠1 + m∠2 = m∠LAN
Step 3: m∠1 + m∠2 = 30⁰
Step 4: m∠1 = 15⁰
Step 5: 15⁰ + m∠2 = 30⁰
Step 6: m∠2 = 15⁰
Step 7: m∠1 = m∠2
Step 8: ∠1 ≅ ∠2
Step 9: AM bisects ∠LAN
What is the justification for Step 9?

Symmetric property of congruence

Definition of angle bisector

Addition property of equality

Definition of congruent angles

Tags

CCSS.HSG.SRT.B.5

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: AC = AB + AB
Prove: AB = BC
Reason 1: Given
Reason 2: Segment addition postulate
What is Step 2?

AC = AB + AB

AB = BC

AB + BC = AC

AB + AB = AB + BC

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: AC = AB + AB
Prove: AB = BC
Reason 1: Given
Reason 2: Segment addition postulate
Reason 3: Transitive property of equality
What is Step 3?

AC = AB + AB

AB = BC

AB + BC = AC

AB + AB = AB + BC

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: ∠1 is a complement of ∠2  and  ∠2 ≅ ∠3
Prove: ∠1 is a complement of ∠3
Reason 1: Given
Reason 2: Given
What is Step 2?

∠2 ≅ ∠3

m∠1 + m∠2 = 90⁰

m∠2 = m∠3

m∠1 + m∠3 = 90⁰

Tags

CCSS.7.G.B.5

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: ∠1 is a complement of ∠2  and  ∠2 ≅ ∠3
Prove: ∠1 is a complement of ∠3
Reason 1: Given
Reason 2: Given
Reason 3: Definition of complementary angles
Reason 4: Definition of congruent angles
What is Step 4?

∠2 ≅ ∠3

m∠1 + m∠2 = 90⁰

m∠2 = m∠3

m∠1 + m∠3 = 90⁰

Tags

CCSS.7.G.B.5

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: ∠1 is a complement of ∠2  and  ∠2 ≅ ∠3
Prove: ∠1 is a complement of ∠3
Reason 1: Given
Reason 2: Given
Reason 3: Definition of complementary angles
Reason 4: Definition of congruent angles
Reason 5: Substitution property of equality
Reason 6: Definition of complement
What is Step 6?

∠1 is a complement of ∠3

m∠1 + m∠2 = 90⁰

m∠2 = m∠3

m∠1 + m∠3 = 90⁰

Tags

CCSS.7.G.B.5

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
What is the justification for Step 1?

Given

Substitution

Angle addition postulate

Definition of congruent angles

Tags

CCSS.HSG.SRT.B.5

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