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Consider the following sets.U = {all triangles}E = {x|x ∈ U and x is equilateral}I = {x|x ∈ U and x is isosceles}S = {x|x ∈ U and x is scalene}A = {x|x ∈ U and x is acute}O = {x|x ∈ U and x is obtuse}R = {x|x ∈ U and x is right}Which is a subset of I?

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Consider the two planes.

line a.

line b.

line d.

plane Q.

Triangles A B C and E D C are shown. Triangle A B C is rotated about point C to form triangle E D C.

a rotation about point B

a reflection across the line containing CB

a reflection across the line containing AC

a rotation about point C

Lines P S and W T are horizontal and parallel. Lines V R and Q R are diagonal and intersect lines P S and W T to form triangle X Y Z.

∠RXZ and ∠YXZ

∠PXQ and ∠RXS

∠YZX and ∠UZT

∠WZX and ∠XYZ

How can ΔABC be mapped to ΔXYZ?

vertex B to vertex Z

vertex B to vertex Y

vertex A to vertex Z

vertex A to vertex Y

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.

h = 1.5

h = 9

h = 10

h = 13.5

Two similar triangles are shown.

translated

reflected

dilated

rotated

Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot

m∠A = 30°, m∠B = 60°, m∠C = 90°

m∠A = 90°, m∠B = 60°, m∠C = 30°

m∠A = 60°, m∠B = 90°, m∠C = 30°

m∠A = 90°, m∠B = 30°, m∠C = 60°

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

16.7°

17.5°

72.5°

73.3°

Quadrilateral FGHJ is dilated according to the ruleDO,(x,y) to create the image quadrilateral F'G'H'J', which is not shown.

(-2,-4)

(-2,-6)

(Negative nine-halves, negative 4)

(Negative nine-halves, negative 9)

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

33.6°

39.8°

50.2°

56.4°

Which diagram has all the correct lines of reflectional symmetry for the rectangle?

A rectangle is folded diagonally on both corners.

A rectangle is folded by a vertical and horizontal line going through its center.

A rectangle is folded 4 ways. It is folded horizontally, vertically, and diagonally on both corners.

A rectangle is folded 4 ways. It is folded diagonally at each midpoint of every side.

In the diagram, .

WV and XY

WV and ZY

∠VZW ≅ ∠YZX

∠VWZ ≅ ∠YXZ

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C.

a reflection and a dilation

a rotation and a dilation

a translation and a dilation

a reflection and a translation

In the diagram, DC is 10 units and BC is 6 units.

6 units

8 units

12 units

16 units

A line extends from a side of a triangle.

a remote interior angle

an adjacent interior angle

an exterior angle

a complementary angle

Triangle ABC has the angle measures shown.

Measure of angle A = 20 degrees

Measure of angle B = 60 degrees

are complementary

Measure of angle A + measure of angle C = 120 degrees

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference.Which choice represents the sample space, S, for this event?

S = {ABC, ABD, ACD, BCD}

S = {ABC, BCA, CDA, DAC}

S = {ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC}

S = {ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC}

Triangle A B C is cut by line segment F G. Line segment F G goes from side A B to side A C. The length of B F is x + 6, the length of F A is x + 1, the length of C G is x + 3, and the length of G A is x minus 1.

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.

Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.

Read the proof.Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°Prove: △HKJ ~ △LNP

CPCTC

definition of supplementary angles

triangle parts relationship theorem

triangle angle sum theorem

A number cube has faces numbered 1 to 6.What is true about rolling the number cube one time? Select three options.S = {1, 2, 3, 4, 5, 6}If A is a subset of S, A could be {0, 1, 2}.If A is a subset of S, A could be {5, 6}.If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.If a subset A represents the complement of rolling an even number, then A = {1, 3}.

S = {1, 2, 3, 4, 5, 6}

If A is a subset of S, A could be {0, 1, 2}.

If A is a subset of S, A could be {5, 6}.

If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.

If a subset A represents the complement of rolling an even number, then A = {1, 3}.

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2.25.

x = 2.25 units

x = 2.5 units

x = 4.25 units

x = 4.5 units

Circle B is inside of circle A.

A = {states in the US}; B = {world countries}

A = {plays by Shakespeare}; B = {playwrights}

A = {animals}; B = {mammals}

A = {polygons}; B = {circles}

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

60 ft

120 ft

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