Exam: 02.08 Transformations and Congruence Review and Practice Test

Rectangle J′K′L′M′ shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.

(16, 7)

Which series of transformations will not map figure Q onto itself?

(x + 0 y − 4), reflection over y = x − 1

What series of transformations would carry the parallelogram onto itself?

(x + 6, y + 0), 180° rotation, (x + 0, y + 4)

Trapezoid ABCD is rotated 90° clockwise. What rule shows the input and output of the reflection, and what is the new coordinate of A′?

(x, y) → ( y, −x); A′ is at (1, 5)

In triangle ABC shown below, side AB is 6 and side AC is 4:Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 3, and segment AE is 2.

The figure below shows rectangle ABCD with diagonals and :Anastasia wrote the following proof to show that the diagonals of rectangle ABCD are congruent:Anastasia's proof:Statement 1: Rectangle ABCD is givenStatement 2: ≅ because opposite sides of a rectangle are congruentStatement 3: ≅ by the reflexive property of congruenceStatement 4:Statement 5: Angles BAD and ADC are congruent because all right angles are congruentStatement 6: Triangles BAD and CDA are congruent by SASStatement 7: ≅ by CPCTCWhich statement below completes Anastasia's proof?

Angles BAD and ADC are 90 degrees (perpendicular lines create 90 degree angles)

Which statement accurately describes how to reflect point A (3, −1) over the y-axis?

Construct a line from A perpendicular to the y-axis, determine the distance from A to the y-axis along this perpendicular line, find a new point on the other side of the y-axis that is equidistant from the y-axis.

Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?

If Line Ac ≅ Line Bc , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects

If triangle MNO is congruent to triangle PQR, which statement is not true?

Line MN ≅ Line QR

If quadrilateral PQRS is a rectangle, then which of the following is true?

Line Ps congruent Line Qr

Triangle HAM is translated using the rule (x, y) → (x + 6, y) to create triangle H′A′M′. If a line segment is drawn from point H to point H′ and from point A to point A′, which statement would best describe the line segments drawn?

They are parallel and congruent.

The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel:A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and BCD are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB ________. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.Which phrase best completes the student's proof?

form a pair of alternate interior angles that are congruent

Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that ≅ and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by ASA?

∠EFG and ∠ONM