Geometry Unit 2 Post-Assessment

In the figure below, Line m and Line n are parallel lines intersected by Line t. Which pair of angles is congruent?

• ∠1 and ∠8

• ∠2 and ∠8

• ∠3 and ∠4

• ∠4 and ∠7

Answer explanation

Lines m and n are parallel, and Line t acts as a transversal. By the properties of parallel lines, ∠2 and ∠8 are corresponding angles, making them congruent. Thus, the correct answer is ∠2 and ∠8.

Tags

CCSS.HSG.CO.C.9

Line a and b are cut by a transversal. What value of x proves a ∥ b?

• 17

• 21

• 33

• 51

Answer explanation

To prove lines a and b are parallel, the consecutive interior angles formed by the transversal must be supplementary.

If x = 21, the angles are equal, confirming a ∥ b. Thus, the correct value of x is 21.

Tags

CCSS.HSG.CO.C.9

• 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.HSG.GPE.B.5

Given: p parallel q. Which of these statements is NOT true?

• m∠1 = m∠4

• m∠2 = m∠6

• m∠6 + m∠3 = 180°

• m∠2 + m∠5 = 180°

Answer explanation

The statement m∠6 + m∠3 = 180° is NOT true because m∠6 and m∠3 are not supplementary angles formed by the parallel lines and a transversal.

The other statements about angles formed by parallel lines are true.

Lines h and g are cut by a transversal. What value of x will prove that line h is parallel to line g?

• 7

• 19

• 12

• 0

Answer explanation

To prove lines h and g are parallel, the corresponding angles formed by the transversal must be equal.

If x = 12, the angles are equal, confirming that line h is parallel to line g.

Tags

CCSS.HSG.CO.C.9

• x = 10, m∠ABC = 50°

• x = 20, m∠ABC = 90°

• x = 20, m∠ABC = 60°

• x = 40, m∠ABC = 120°

Answer explanation

Since p is parallel to q, ∠ABC is an alternate interior angle. Given the choices, x must be 20 to satisfy the angle condition, making m∠ABC = 60°. Thus, the correct answer is x = 20, m∠ABC = 60°.

Tags

CCSS.HSG.C.A.2

CCSS.HSG.GPE.B.5

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

• A. ( 90°, 70°, 20° )

• B. ( 90°, 62°, 38° )

• C. ( 90°, 60°, 30° )

• D. ( 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.HSG.CO.C.10

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.D.11

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.HSG.CO.C.9

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.HSG.CO.C.9

If k || m, what is the value of y? (Figure is not drawn to scale.)

• 15°

• 65°

• 115°

• 120°

Answer explanation

Since k || m, consecutive exterior angles are supplementary. Solve the equation for x.

Replace x with 15 in the expression 3x + 20 to get 65°.

The angles on a straight line sum to 180°, so y = 180° - 65° = 115°. Thus, the value of y is 115°.

Tags

CCSS.HSG.GPE.B.5