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

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

Describe the difference between a postulate and a theorem.

Evaluate responses using AI:

OFF

Answer explanation

A postulate is assumed to be true without proving it.

A theorem is true and can be proven.

Complete the two-column proof.

i

h

g

f

Addition Property of Equality

Def. of Congruence

Angle Addition Property (2nd time)

Angle Addition Property (1st time)

Given

m∠ABC=m∠DEF

Reflexive Property

Substitution Property

Angle Addition Property

Transitive Property

Answer explanation

Perpendicular/Parallel Line Theorem:

draw a sketch to illustrate the theorem.

Answer explanation

State the Perpendicular/Parallel Line Theorem.

Evaluate responses using AI:

OFF

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.

Complete the 2-column proof

c

g

i

Prove

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Same-side Interior Angles Therorem

Given

Suppl. of the same angle are congruent

Corresponing Angles Converse Theorem

Answer explanation

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