Line and Angle Relationships

In the figure, two angles are marked congruent.

Which theorem justifies the conclusion that m ‖ n?

• Alternate Exterior Angles Theorem

• Alternate Exterior Angles Converse Theorem

• Corresponding Angles Converse Theorem

• Vertical Angle Theorem

Tags

TEKS G.6A

Consider the proof of the Same-Side Interior Angles Theorem.

Given: ℓ ‖ m

Prove: ∠2 and ∠5 are supplementary

Which missing reasons correctly complete the proof?

• (2) Corresponding Angles Theorem (7) Substitution Property of Equality

• (2) Same-Side Interior Angles Theorem

  (7) Substitution Property of Equality

• (2) Corresponding Angles Theorem (7) Definition of supplementary angles

• (2) Same-Side Interior Angles Theorem (7) Definition of supplementary angles

Tags

CCSS.8.G.A.5

Which of the following statements is false?

• Vertical angles are always congruent.

• When a pair of lines is cut by a transversal, the corresponding angles are always congruent.

• Inscribed angles that intercept the same arc are always congruent

• All right angles are congruent.

Consider the proof of the Alternate Interior Angles Theorem.

Given: ℓ ‖ m

Prove: ∠2 and ∠8 are congruent.

Which missing reasons correctly complete the proof?

• (2) Corresponding Angles Theorem (3) Transitive Property of Congruence

• (2) Same-Side Interior Angles Theorem (3) Vertical Angle Theorem

• (2) Corresponding Angles Theorem (3) Vertical Angle Theorem

• (2) Same-Side Interior Angles Theorem (3) Transitive Property of Congruence

Tags

CCSS.8.G.A.5

Describe the difference between a postulate and a theorem.

Answer explanation

A postulate is assumed to be true without proving it.

A theorem is true and can be proven.

Tags

CCSS.8.G.A.5

Complete the two-column proof.

i

h

g

f

Transitive Property

Angle Addition Property (1st time)

Angle Addition Property

Reflexive Property

Addition Property of Equality

m∠ABC=m∠DEF

Def. of Congruence

Angle Addition Property (2nd time)

Given

Substitution Property

Answer explanation

Tags

CCSS.HSG.SRT.B.5

Perpendicular/Parallel Line Theorem:

draw a sketch to illustrate the theorem.

Answer explanation

State the Perpendicular/Parallel Line Theorem.

Answer explanation

The Perpendicular/Parallel Line Theorem states that if two lines are perpendicular to the same line, then two lines are parallel to each other.

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Complete the 2-column proof

c

g

i

Same-side Interior Angles Therorem

Alternate Interior Angles Theorem

Prove

Given

Corresponing Angles Converse Theorem

Corresponding Angles Theorem

Suppl. of the same angle are congruent

Answer explanation

Tags

CCSS.8.G.A.5

In the figure, the measure of angle 8 is 74°.

Which angle needs to be equal to 106° for lines n and m to be parallel by the Same-Side Exterior Angles Converse Theorem? ​ (a)   ​

• angle 1
• angle 2
• angle 3
• angle 4
• angle 5
• angle 6
• angle 7

Tags

CCSS.8.G.A.5