Geometry Quiz

Select all of the following transformations that preserve distance.

• Reflection over the y-axis

• (x, y) → (x, –y)

• Rotation 90° clockwise about the origin

• (x, y) → (6x, 6y)

• Dilation with scale factor 0.5 centered at the origin

Use the Law of Detachment to make a conclusion. If a point is on the perpendicular bisector of a line segment, then the point is equidistant from the segment’s endpoints. The midpoint of AB is X. XY is perpendicular to AB. Point L is on XY.

• Point L is not on the perpendicular bisector of AB.

• Point L is equidistant to points X and Y.

• Point L is equidistant from points A and B.

• Point L is not equidistant from points A and B.

In ΔABC, point D is the midpoint of AC. Fill in the blanks to prove the Isosceles Triangle Theorem.

• Given: AB ≅ BC Prove: ∠A ≅ ∠C It is given that AB ≅ BC. By the Reflexive Property BD ≅ BD. Since D is the midpoint of AC, AD ≅ DC. So ΔABD ≅ ΔCBD by SAS. Therefore ∠A ≅ ∠C by CPCTC.

• Given: AB ≅ AC Prove: ∠B ≅ ∠C It is given that AB ≅ AC. By the Reflexive Property BD ≅ BD. Since D is the midpoint of BC, BD ≅ DC. So ΔABD ≅ ΔCDB by SAS. Therefore ∠B ≅ ∠C by CPCTC.

• Given: AC ≅ BC Prove: ∠A ≅ ∠B It is given that AC ≅ BC. By the Reflexive Property AD ≅ AD. Since D is the midpoint of AB, AD ≅ DB. So ΔACD ≅ ΔBCD by SAS. Therefore ∠A ≅ ∠B by CPCTC.

• Given: AB ≅ BC Prove: ∠B ≅ ∠C It is given that AB ≅ BC. By the Reflexive Property AC ≅ AC. Since D is the midpoint of AB, AD ≅ DB. So ΔABD ≅ ΔCBD by SAS. Therefore ∠B ≅ ∠C by CPCTC.

The angle bisector of ∠ABC is BP. If m∠ABP = 6n, what is m∠ABC?

• 12

• 3n

• 12n

• 36n²

Select all the pairs of angles that are alternate interior angles.

• A. ∠1 and ∠3

• B. ∠5 and ∠6

• C. ∠8 and ∠9

• D. ∠8 and ∠17

• E. ∠16 and ∠17

Point B has coordinates (−8, 1). What are the coordinates of the point when reflected across the y-axis and then rotated 180° about the origin?

• A. (8, 1)

• B. (−8, −1)

• C. (−8, 1)

• D. (8, −1)

Select all the equations that represent a line that is perpendicular to the line with equation y = 2x − 8.

• A. y = 1/2 x + 1

• B. y = −1/2 x + 1

• C. x + 2y = 5

• D. −x + 2y = −3

• E. −x − 2y = 9

Quadrilateral ABCD has coordinates A(−2, 0), B(0, 4), C(4, 6), and D(2, 2). What are the coordinates of the image of ABCD after applying the transformation (x, y) → (−x, y) and then applying (x, y) → (x, −y)?

• A'(2, 0), B'(0, -4), C'(-4, -6), D'(-2, -2)

• A'(2, 0), B'(0, 4), C'(-4, 6), D'(-2, 2)

• A'(-2, 0), B'(0, -4), C'(4, -6), D'(2, -2)

• A'(-2, 0), B'(0, 4), C'(4, 6), D'(2, 2)

What rule maps ABCD to A'B'C'D'?

• A. r_y-axis ∘ T_(-1,0)

• B. r_x-axis ∘ T_(1,0)

• C. T_(0,-1) ∘ r_y-axis

• D. T_(0,1) ∘ r_x-axis

ΔABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B' after the transformation (x, y) → (−y, x), then translation 1 unit right and 4 units up?

• (0, 3)

• (3, 0)

• (1, 4)

• (4, 1)