2.08 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.What will be the location of T′ in the image trapezoid S′T′U′V′?

(18, 2)

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

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

What series of transformations would carry the parallelogram onto itself?

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

Parallelogram ABCD is rotated 90° counterclockwise. What rule shows the input and output of the rotation, 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 10 and side AC is 8:Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 5, and segment AE is 4.

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC, and side AD is parallel to side BC:A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal:For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by ________. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC.Which phrase best completes the student's proof?

ASA Postulate

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 both right angles (definition of a rectangle)

Which statement accurately describes how to reflect point A (−2, 1) over the x‐axis?

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

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.

Triangle ABC is a right triangle. Point D is the midpoint of side AB, and point E is the midpoint of side AC. The measure of ∠ADE is 47°.The proof, with a missing reason, proves that the measure of ∠ECB is 43°. StatementReasonm∠ADE = 47°Givenm∠DAE = 90°Definition of a right anglem∠AED = 43°? joins the midpoints of and Given is parallel to Midsegment of a Triangle Theorem∠ECB ≅ ∠AEDCorresponding angles are congruentm∠ECB = 43°Substitution property Which theorem can be used to fill in the missing reason?

Triangle Sum Theorem

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

segment MN ≅ segment QR

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

segment SQ ≅ segment PR