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

(13, −1)

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 trapezoid onto itself?

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

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

(x − 3, y − 3), reflection over y = −x + 2

Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?

(x, y) → (−x, −y); A′ is at (5, −1)

In triangle DEF, if m∠D = (4x)°, m∠E = (2x − 3)°, and m∠F = (x + 8)°, what is the value of x?

25

Triangles ABD and CBD are shown. If m∠ADB = 110°, what is the relationship between AB and BC?

AB > BC

If triangle GHI is congruent to triangle JKL, which statement is not true?

GH ≅ KL

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 m∠ACD = 90° 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?

MN≅QR

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 angle ADE is 36°. The proof, with a missing reason, proves that the measure of angle ECB is 54°. Which theorem can be used to fill in the missing reason?

Midsegment of a Triangle Theorem

Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A′ is at (−4, 2) and the image of D′ is at (−2, 1). Which transformation can be used to show that ABCDE and its image are congruent?

Rotate ABCDE 90° counterclockwise.

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent 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 CDB. Therefore, the triangles ABD and CDB are congruent by ________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?

SAS Postulate

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.

In triangle ABC shown below, side AB is 8 and side AC is 4 Which statement is needed to prove that segment DE is half the length of segment BC?

Segment AD is 4, and segment AE is 2.

The figure below shows rectangle ABCD with diagonals AC and BD Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Statement 1: Rectangle ABCD is given Statement 2: AD ≅ BC because opposite sides of a rectangle are congruent Statement 3: DC ≅ DC by the reflexive property of congruence Statement 4: Angles ADC and BCD are both right angles by definition of a rectangle Statement 5: Angles ADC and BCD are congruent because all right angles are congruent Statement 6: Statement 7: AC ≅ BD by CPCTC Which statement below completes Zinnia's proof?

Triangles ADC and BCD are congruent (by SAS postulate)

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 equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB 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

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

∠STP ≅ ∠QTR