Question 1

In the diagram below, $\bigtriangleup ABC$ is reflected over line $ℓ$ to create $\bigtriangleup DEF$ .

If $m∠A=40°$ and $m∠B=95°$ , what is $m∠F$ ?

Accepted Answer

Answer

Answer

Answer

Question 2

The diagram below shows triangle $\bigtriangleup ABC$ with point $ℓ$ on side $\bigtriangleup DEF$ and point $Y$ on side $\overline{\mathrm{CB}}$ .

Which information is sufficient to prove that $m∠F$ ?

Accepted Answer

$45°$ is parallel to $\overline{\mathrm{AC}}$ .

Answer

$45°$ is isosceles

Answer

<math>\overline{\mathrm{AX}}\ \cong\ \overline{\mathrm{CY}}</math>

Answer

$45°$ is a right angle.

Question 3

Quadrilateral $\bigtriangleup ABC$ is congruent to quadrilateral $ℓ$ . Which statement is always true?

Accepted Answer

Quadrilateral $\bigtriangleup ABC$ can be mapped onto quadrilateral $ℓ$ using a sequence of rigid motions.

Answer

Answer

Quadrilateral $\bigtriangleup ABC$ and quadrilateral $ℓ$ are the same shape, but not necessarily the same size.

Answer

Question 4

A quadrilateral has diagonals that are perpendicular but not congruent. This quadrilateral could be

Accepted Answer

a rhombus

Answer

a rectangle

Answer

a square

Answer

an isosceles trapezoid

Question 5

Which regular polygon has a minimum rotation of $\bigtriangleup ABC$ about its center that carries the polygon onto itself?

Accepted Answer

decagon

Answer

nonagon

Answer

octagon

Answer

pentagon

Question 6

On the set of axes below, $\bigtriangleup ABC$ is the image of $ℓ$ after a dilation centered at point $\bigtriangleup DEF$ .

The scale factor of the dilation that maps $m∠A=40°$ onto $m∠B=95°$ is

Accepted Answer

Answer

Answer

Answer

Question 7

In the diagram of $\bigtriangleup ABC$ below, $ℓ$ , $\bigtriangleup DEF$ , and $Y$ .

What is the measure of $m∠B=95°$ , to the nearest degree?

Accepted Answer

Answer

Answer

Answer

Question 8

The Pyramid of Memphis, in Tennessee, stands $\bigtriangleup ABC$ yards tall and has a square base whose side is $ℓ$ yards long.

What is the volume of the Pyramid of Memphis, to the nearest cubic yard?

Accepted Answer

Answer

Answer

Answer

Question 9

A square is graphed on the set of axes below, with vertices at $\bigtriangleup ABC$ and $ℓ$ .

Which transformation would not carry the square onto itself?

Accepted Answer

reflection over the y-axis

Answer

reflection over the line $\bigtriangleup ABC$

Answer

rotation of $\bigtriangleup ABC$ degrees around point $ℓ$

Answer

reflection over the x-axis

Question 10

If scalene triangle $\bigtriangleup ABC$ is similar to triangle $ℓ$ and $\bigtriangleup DEF$ , which equation is always true?

Accepted Answer

Answer

Answer

Answer

Question 11

A plane intersects a cylinder perpendicular to its bases.

This cross section can be described as a

Accepted Answer

rectangle

Answer

parabola

Answer

circle

Answer

triangle

Question 12

An equation of line $\bigtriangleup ABC$ is $ℓ$ . An equation of line $\bigtriangleup DEF$ is $Y$ . Which statement about lines $\overline{\mathrm{CB}}$ and $q$ is true?

Accepted Answer

Line $\bigtriangleup ABC$ is not the image of line $ℓ$ after a dilation because the lines are not parallel.

Answer

A dilation of $\bigtriangleup ABC$ centered at the origin will map line $ℓ$ onto line $\bigtriangleup DEF$ .

Answer

A dilation of $\bigtriangleup ABC$ centered at the origin will map line $ℓ$ onto line $\bigtriangleup DEF$ .

Answer

Line $\bigtriangleup ABC$ is not the image of line $ℓ$ after a dilation because the lines do not pass through the origin.

Question 13

The coordinates of the endpoints of $\bigtriangleup ABC$ are $ℓ$ and $\bigtriangleup DEF$ . If point $Y$ is on $\overline{\mathrm{CB}}$ , what are the coordinates of $q$ such that $SM:MC$ is $1:2$ ?

Accepted Answer

Answer

Answer

Answer

<math>\left(-\frac{5}{2},-\frac{3}{2}\right)</math>

Question 14

On the set of axes below, rectangle $\bigtriangleup ABC$ has vertices with coordinates $ℓ$ and $\bigtriangleup DEF$ .

What is the area of rectangle $m∠A=40°$ ?

Accepted Answer

Answer

Answer

Answer

Question 15

In parallelogram $\bigtriangleup ABC$ shown below, $ℓ$ bisects $\bigtriangleup DEF$ .

If $m∠A=40°$ , then $m∠B=95°$ is

Accepted Answer

Answer

Answer

<math>70\degree</math>

Answer

Question 16

In right triangles $\bigtriangleup ABC$ and $ℓ$ , hypotenuse $\bigtriangleup DEF$ and hypotenuse $Y$ . If $\overline{\mathrm{CB}}$ , then $q$ is the ratio of the corresponding

Accepted Answer

areas

Answer

perimeters

Answer

legs

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volumes

Question 17

Parallelogram $\bigtriangleup ABC$ with diagonal $ℓ$ is drawn below. Line segment $\bigtriangleup DEF$ is drawn such that it bisects $Y$ at $\overline{\mathrm{CB}}$ .

Which triangle congruence method would prove that $m∠F$ ?

Accepted Answer

both ASA and AAS

Answer

ASA&#44; only

Answer

neither ASA nor AAS

Answer

AAS&#44; only

Question 18

In the diagram below of circle $\bigtriangleup ABC$ , chords $ℓ$ and $\bigtriangleup DEF$ intersect at $Y$ , and chords $\overline{\mathrm{CB}}$ and $q$ are drawn.

Which statement must always be true?

Accepted Answer

<math>\angle A\cong\angle C</math>

Answer

<math>\angle B\cong\angle C</math>

Answer

<math>\overline{\mathrm{AD}}\cong\overline{\mathrm{BC}}</math>

Answer

<math>\overline{\mathrm{AB}}\cong\overline{\mathrm{CD}}</math>

Question 19

What are the coordinates of the center and length of the radius of the circle whose equation is $\bigtriangleup ABC$ ?

Accepted Answer

center $\bigtriangleup ABC$ and radius $ℓ$

Answer

center $\bigtriangleup ABC$ and radius $ℓ$

Answer

center $\bigtriangleup ABC$ and radius $ℓ$

Answer

center $\bigtriangleup ABC$ and radius $ℓ$

Question 20

In the diagram below, $\bigtriangleup ABC$ is a rectangle, and diagonal $ℓ$ is drawn. Line $\bigtriangleup DEF$ , a vertical line of symmetry, and line $Y$ , a horizontal line of symmetry, intersect at point $\overline{\mathrm{CB}}$ .

Which sequence of transformations will map $m∠F$ onto $\bigtriangleup CDB$ ?

Accepted Answer

a reflection over line $\bigtriangleup ABC$ followed by a reflection over line $ℓ$

Answer

a reflection over line $\bigtriangleup ABC$ followed by a $ℓ$ rotation about point $\bigtriangleup DEF$

Answer

a $\bigtriangleup ABC$ rotation about point $ℓ$

Answer

a reflection over $\bigtriangleup ABC$

Question 21

The diagram below models a countertop designed for a kitchen. The countertop is made of solid oak and is $\bigtriangleup ABC$ inches thick.

If oak weighs approximately $44$ pounds per cubic foot, the approximate weight, in pounds, of the countertop is

Accepted Answer

Answer

Answer

Answer

Question 22

In the diagram below of $\bigtriangleup ABC$ , $ℓ$ intersects $\bigtriangleup DEF$ and $Y$ at points $\overline{\mathrm{CB}}$ and $q$ respectively, and $SM:MC$ .

If $AT=4,\ BC=18,\ TB=5,$ and $AV=6$ , what is the perimeter of quadrilateral $TBCV$ ?

Accepted Answer

Answer

Answer

Answer

Question 23

A circle centered at the origin passes through $\bigtriangleup ABC$ .

What is the equation of the line tangent to the circle at $44$ ?

Accepted Answer

<math>y-4=\frac{3}{4}\left(x+3\right)</math>

Answer

<math>y+4=\frac{3}{4}\left(x-3\right)</math>

Answer

<math>y-4=\frac{4}{3}\left(x+3\right)</math>

Answer

<math>y+4=\frac{4}{3}\left(x-3\right)</math>

Question 24

In the diagram below, quadrilateral $\bigtriangleup ABC$ is inscribed in circle $ℓ$ , $\bigtriangleup DEF$ , $Y$ , and $\overline{\mathrm{CB}}$ .

What is $m∠F$ ?

Accepted Answer

Answer

Answer

Answer

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