Question 1

In the diagram below, $\Delta ABC\cong\Delta DEF$ .

Which sequence of transformations maps $\Delta ABC$ onto $\Delta DEF$ ?

Accepted Answer

a reflection over the $\Delta ABC\cong\Delta DEF$ -axis followed by a translation

Answer

a counterclockwise rotation of $\Delta ABC\cong\Delta DEF$ about the origin followed by a translation

Answer

a rotation of $\Delta ABC\cong\Delta DEF$ about the origin followed by a translation

Answer

a reflection over the $\Delta ABC\cong\Delta DEF$ -axis followed by a translation

Question 2

On the set of axes below, the vertices of $\Delta ABC\cong\Delta DEF$ have coordinates $P(-6,7)$ , $Q(2,1)$ , and $R(-1,-3)$ .

What is the area of $\Delta PQR$ ?

Accepted Answer

Answer

Answer

Answer

Question 3

In right triangle $\Delta ABC\cong\Delta DEF$ , $P(-6,7)$ . If $Q(2,1)$ , which function also equals $R(-1,-3)$ ?

Accepted Answer

Answer

Answer

Answer

Question 4

In the diagram below, $\Delta ABC\cong\Delta DEF$ .

What is the number of degrees in the measure of $\Delta ABC$ ?

Accepted Answer

<math>46\degree</math>

Answer

<math>92\degree</math>

Answer

<math>134\degree</math>

Answer

<math>68\degree</math>

Question 5

Given $\Delta ABC\cong\Delta DEF$ shown below, with trapezoid $P(-6,7)$ , $Q(2,1)$ , $R(-1,-3)$ , and $PO=4$ .

What is the length of $\overline{\mathrm{TR}}$ ?

Accepted Answer

Answer

Answer

Answer

Question 6

A line segment is dilated by a scale factor of $\Delta ABC\cong\Delta DEF$ centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

Accepted Answer

The line segments are parallel, and the image is twice the length of the given line segment.

Answer

The line segments are parallel, and the image is one-half of the length of the given line segment.

Answer

The line segments are perpendicular, and the image is one-half of the length of the given line segment.

Answer

The line segments are perpendicular, and the image is twice the length of the given line segment.

Question 7

Which figure always has exactly four lines of reflection that map the figure onto itself?

Accepted Answer

square

Answer

rectangle

Answer

regular octagon

Answer

equilateral triangle

Question 8

In the diagram below of circle $\Delta ABC\cong\Delta DEF$ , chord $P(-6,7)$ bisects chord $Q(2,1)$ at $R(-1,-3)$ .

If $\Delta PQR$ and $\overline{\mathrm{TR}}$ is $5$ more than $DE$ , then $FE$ is

Accepted Answer

Answer

Answer

Answer

Question 9

Kelly is completing a proof based on the figure below.

She was given that $∠A\cong∠EDF$ , and has already proven $\Delta ABC$ . Which pair of corresponding parts and triangle congruency method would not prove $\Delta ABC\cong\Delta DEF$ ?

Accepted Answer

$25$ and SAS

Answer

$25$ and AAS

Answer

$25$ and SAS

Answer

$25$ and ASA

Question 10

In the diagram below, $\Delta ABC\cong\Delta DEF$ divides $P(-6,7)$ and $Q(2,1)$ proportionally, $R(-1,-3)$ , $PO=4$ , and $\overline{\mathrm{DF}}$ bisects $\angle BDE$ .

The measure of angle $DE$ is

Accepted Answer

Answer

Answer

Answer

Question 11

Which set of statements would describe a parallelogram that can always be classified as a rhombus?

$I.$ Diagonals are perpendicular bisectors of each other.

$\Delta ABC$ Diagonals bisect the angles from which they are drawn.

$R(-1,-3)$ Diagonals form four congruent isosceles right triangles.

Accepted Answer

$25$ , $∠A\cong∠EDF$ , and $\Delta ABC$

Answer

$25$ and $∠A\cong∠EDF$

Answer

$25$ and $∠A\cong∠EDF$

Answer

$25$ and $∠A\cong∠EDF$

Question 12

The equation of a circle is $\Delta ABC\cong\Delta DEF$ . What are the coordinates of the center and the length of the radius of the circle?

Accepted Answer

center $\Delta ABC\cong\Delta DEF$ and radius $P(-6,7)$

Answer

center $\Delta ABC\cong\Delta DEF$ and radius $P(-6,7)$

Answer

center $\Delta ABC\cong\Delta DEF$ and radius $P(-6,7)$

Question 13

In the diagram of $\Delta ABC\cong\Delta DEF$ below, $P(-6,7)$ , $Q(2,1)$ , and $R(-1,-3)$ .

What is the measure of $\Delta PQR$ , to the nearest degree?

Accepted Answer

<math>23\degree</math>

Answer

<math>43\degree</math>

Answer

<math>67\degree</math>

Answer

<math>47\degree</math>

Question 14

Triangle $\Delta ABC\cong\Delta DEF$ is the image of $P(-6,7)$ after a dilation followed by a translation.

Which statement(s) would always be true with respect to this sequence of transformations?

$R(-1,-3)$

$PO=4$

$\overline{\mathrm{DF}}$

$\angle BDE$

Accepted Answer

$25$ and $∠A\cong∠EDF$

Answer

$25$ , only

Answer

$25$ , $∠A\cong∠EDF$ , and $\Delta ABC$

Answer

$25$ and $∠A\cong∠EDF$

Question 15

Line segment $\Delta ABC\cong\Delta DEF$ has endpoints $P(-6,7)$ and $Q(2,1)$ . Point $R(-1,-3)$ is on $PO=4$ such that $\overline{\mathrm{DF}}$ is $\angle BDE$ . What are the coordinates of point $P$ ?

Accepted Answer

Answer

Answer

Answer

Question 16

The pyramid shown below has a square base, a height of $\Delta ABC\cong\Delta DEF$ , and a volume of $P(-6,7)$ .

What is the length of the side of the base?

Accepted Answer

Answer

Answer

Answer

Question 17

In the diagram below of triangle $\Delta ABC\cong\Delta DEF$ , $P(-6,7)$ and $Q(2,1)$ are bisected by $R(-1,-3)$ and $PO=4$ , respectively. Segments $\overline{\mathrm{DF}}$ and $\angle BDE$ intersect at $P$ , and $m∠N=40°$ .

If $m∠TMR=28°$ , the measure of angle $OTS$ is

Accepted Answer

Answer

Answer

Answer

Question 18

In the diagram below, right triangle $\Delta ABC\cong\Delta DEF$ has legs whose lengths are $P(-6,7)$ and $Q(2,1)$ .

What is the volume of the three-dimensional object formed by continuously rotating the right triangle around $\Delta ABC\cong\Delta DEF$ ?

Accepted Answer

Answer

Answer

Answer

Question 19

What is an equation of a line that is perpendicular to the line whose equation is $\Delta ABC\cong\Delta DEF$ and passes through $P(-6,7)$ ?

Accepted Answer

Answer

Answer

Answer

Question 20

In quadrilateral $\Delta ABC\cong\Delta DEF$ shown below, $P(-6,7)$ .

Which information would be sufficient to prove quadrilateral $\Delta DEF$ is a parallelogram?

Accepted Answer

<math>\overline{\mathrm{LU}}\parallel\overline{\mathrm{BE}}</math>

Answer

<math>\overline{\mathrm{BE}}\cong\overline{BL}</math>

Answer

<math>\overline{\mathrm{LU}}\cong\overline{\mathrm{EU}}</math>

Answer

<math>\overline{\mathrm{BL}}\parallel\overline{\mathrm{EU}}</math>

Question 21

A ladder $\Delta ABC\cong\Delta DEF$ feet long leans against a building, forming an angle of $P(-6,7)$ with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

Accepted Answer

Answer

Answer

Answer

Question 22

In the two distinct acute triangles $\Delta ABC\cong\Delta DEF$ and $P(-6,7)$ , $Q(2,1)$ . Triangles $R(-1,-3)$ and $PO=4$ are congruent when there is a sequence of rigid motions that maps

Accepted Answer

$25$ onto $∠A\cong∠EDF$ , and $\Delta ABC$ onto $\Delta DEF$

Answer

$25$ onto $∠A\cong∠EDF$ , and $\Delta ABC$ onto $\Delta DEF$

Answer

point $\Delta ABC\cong\Delta DEF$ onto point $P(-6,7)$ , and $Q(2,1)$ onto $R(-1,-3)$

Answer

$25$ onto $∠A\cong∠EDF$ , and $\Delta ABC$ onto $\Delta DEF$

Question 23

A fabricator is hired to make a $\Delta ABC\cong\Delta DEF$ -foot-long solid metal railing for the stairs at the local library. The railing is modeled by the diagram below. The railing is $P(-6,7)$ inches high and $Q(2,1)$ inches wide and is comprised of a rectangular prism and a half-cylinder.

How much metal, to the nearest cubic inch, will the railing contain?

Accepted Answer

Answer

Answer

Answer

Question 24

In the diagram below, $\Delta ABC\cong\Delta DEF$ and $P(-6,7)$ .

Which statement is not sufficient to prove $\Delta DEF$ ?

Accepted Answer

$25$ and $∠A\cong∠EDF$

Answer

$25$ and $∠A\cong∠EDF$

Answer

<math>\overline{\mathrm{AB}}\parallel\overline{\mathrm{ED}}</math>

Answer

$25$ , $∠A\cong∠EDF$ , $\Delta ABC$ , and $\Delta DEF$

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