Challenging Problems with Parallel Lines Geometry

In the following diagram line r is parallel to line s. Which of the following statements must be true?

• m∠3=m∠5
• m∠5=m∠4
• m∠2 + m∠3 = 180˚
• m∠2=m∠4

Tags

CCSS.8.G.A.5

Given: line t II line s and neither is perpendicular to line g.  Which of the following is false?

• m∠2 + m∠5 = 180°
• m∠1 = m∠7
• m∠3 + m∠5 = 180°
• m∠2 = m∠3

Tags

CCSS.8.G.A.5

In the diagram YT is parallel to MV and m∠YRH = 100°.   Which of the following conclusions does not have to be true?

• m∠MHF = 100°
• m∠RHM = 80°
• ∠SRT and ∠MHF are alternate exterior angles
• ∠SRY and ∠RHV are alternate interior angles

Tags

CCSS.8.G.A.5

Based on the diagram, which theorem or postulate would support the statement m∠RIP = m∠SMY?

• Alternate Exterior Angles Theorem
• Alternate Interior Angles Theorem
• Consecutive Interior Angles Theorem
• Corresponding ∠s Postulate

Tags

CCSS.8.G.A.5

In the diagram below ∠2≅∠3.  Which of the following must be true?

• r ⊥ t
• m∠8 = m∠6
• m∠4 = m∠6
• m∠5 = m∠6

Tags

CCSS.8.G.A.5

Which type of angles are a counterexample to the conjecture below?
"If two lines are parallel, then each pair of angles are supplementary."

• ∠1, ∠2
• ∠3, ∠1
• ∠4, ∠2
• ∠1, ∠4

Tags

CCSS.8.G.A.5

In the diagram below, m∠6 + m∠7 = 180°.  Which of the following does not have to be true?

• m∠1 + m∠4 = 180°
• m∠5 + m∠4 = 180°
• r ∥ s
• m∠2 = m∠7

Tags

CCSS.8.G.A.5

Allison wanted to solve for x, so she set up the equation (5x − 2)° + (3x + 12)° = 180°.  What would her reasoning be?
"If two parallel lines are intersected by a transversal, then ...

• linear pairs are supplementary."
• corresponding angles are supplementary."
• alternate interior angles are congruent."
• consecutive (same-side) interior angles are supplementary."

Tags

CCSS.8.G.A.5

In the diagram below, which pair of angles are alternate interior angles?

• ∠TRM and ∠TGM
• ∠HTL and ∠YGL
• ∠JMG and ∠SGL
• ∠KRT and ∠HTG

Tags

CCSS.8.G.A.5

Use the diagram to determine which pair of angles is alternate exterior angles.

• ∠1 and ∠15
• ∠9 and ∠15
• ∠4 and ∠11
• ∠2 and ∠8

Tags

CCSS.8.G.A.5