Geometry Post Assessment

Identify all angles that are congruent to ∠2, given m ∥ n.

• ∠6

• ∠7

• ∠5

• ∠3

• ∠8

Answer explanation

Since m ∥ n, ∠2 is congruent to ∠3 (vertical angle) and therefore ∠6 and ∠7 (corresponding angles).

Thus, the angles congruent to ∠2 are ∠3, ∠6, and ∠7.

Tags

CCSS.8.G.A.5

Complete the proof with justifications for statement 4: ∠1 ≅ ∠3. Use the draggable options to fill in the blank.

• ∠1 ≅ ∠3

• ∠1 ≅ ∠2

• ∠2 ≅ ∠3

• ∠1 ≅ ∠4

Answer explanation

To prove ∠1 ≅ ∠3, we can use the fact that if ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then by the transitive property of congruence, ∠1 ≅ ∠3. Therefore, the correct choice is ∠1 ≅ ∠3.

Tags

CCSS.7.G.B.5

• 128°

• 90°

• 52°

• 38°

Answer explanation

Since line p is parallel to line j, transversal t forms corresponding angles with the 52 degree angle.

Given the configuration, m∠BAC is 38°, making it the correct choice.

Tags

CCSS.8.G.A.5

What are the measures of the three angles of the triangular shopping district?

• ( 90°, 70°, 20° )

• ( 90°, 62°, 38° )

• ( 90°, 60°, 30° )

• ( 100°, 30°, 20° )

Answer explanation

The sum of angles in a triangle is always 180°. Option A (90°, 70°, 20°) adds up to 180°, making it valid. Other options do not sum to 180°, thus A is the correct choice.

Tags

CCSS.8.G.A.5

Four lines and four congruent angles are identified in the diagram. Which statement must be true?

• Only r ∥ s

• Only a ∥ b

• a ∥ b and r ∥ s

• No pair of lines is parallel.

Answer explanation

The diagram shows four lines with four congruent angles, indicating that lines r and s are parallel due to the alternate interior angles formed.

Lines a and b are not parallel because consecutive interior (or exterior) angles are not suppplementary.

Thus, the only true statement is 'Only r ∥ s'.

Tags

CCSS.8.G.A.5

Which equation can be used to prove the line segments are parallel?

• 118 - w = x

• 118 - x = w

• x + 118 = 180

• w + 118 = 180

Answer explanation

The equation w + 118 = 180 indicates that the angle formed with w is supplementary to 118 degrees. The angles are consecutive interior.

If two angles are supplementary, the lines they form are parallel, making this the correct choice.

Tags

CCSS.8.G.A.5

Andrew cut a rectangular piece of wood along a straight line, as shown below. Andrew calculated that x = 70°. Which of the following statements justifies Andrew’s calculations?

• Vertical angles are congruent

• Alternate exterior angles are congruent

• Consecutive interior angles are supplementary

• Adjacent angles formed by perpendicular lines are complementary

Answer explanation

Andrew's calculation of x = 70° is justified because consecutive interior angles are supplementary.

This means that if one angle is 70°, the adjacent angle must be 110° to sum to 180°, confirming the relationship.

Tags

CCSS.7.G.B.5

Which diagram shows a pair of angle measures that prove lines a and b are parallel?

• A

• B

• C

• D

Answer explanation

Diagram B shows consecutive exterior angles that are supplementary, which is a condition for proving lines a and b are parallel.

This confirms that the correct choice is B.

Tags

CCSS.8.G.A.5

The line on the grid contains points (−4,−1) and (4,−3). Circle all points that lie on the line that passes through the point located at (8,4) and is parallel to the given line.

• (4, 3)

• (2, 5)

• (-1, 8)

• (4, 5)

• (-4, 7)

Answer explanation

The slope of the line through (−4,−1) and (4,−3) is -1/4.

A line parallel to it through (8,4) has the same slope. The points (4,5) and (-4,7) satisfy the equation of this parallel line.

Complete the proof with justifications for statement 4:

• Alternate Exterior Angle Theorem

• Corresponding Angle Converse

• Congruent Supplements Theorem

• Linear Pair Theorem

• Alternate Interior Angles Converse

Answer explanation

The Congruent Supplements Theorem states that if two angles are supplements of the same angle, then they are congruent. Since angles 1 and 3 are both supplementary to the same angle, they must be congruent.

Tags

CCSS.8.G.A.5