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Transformations Tessellations and Fractals

Geometric Properties

Special Right Triangles

Transformations on a Grid

100 100 100 100

200 200 200 200

300 300 300 300

400 400 400 400

500 500 500 500

Final Jeopardy

Jeopardy Board

Board Answer

Transformations Tessellations and Fractals 100The figure below shows the positions of a surveying crew measuring the distance to a tree across the river. Which of the following best represents the measure of TAP?A 58°B 69°C 90°D 122°

Board

Transformations Tessellations and Fractals 100The figure below shows the positions of a surveying crew measuring the distance to a tree across the river. Which of the following best represents the measure of TAP?A 58°B 69°C 90°D 122°

Board Answer

Transformations Tessellations and Fractals 200The figure below shows Aaron’s recent hiking course, which started at point L, went to point M and then point P, and then returned to point L. What is the measure of LMP formed by Aaron’s hiking course?

A 101°B 79°C 54°D 43°

Board

Transformations Tessellations and Fractals 200The figure below shows Aaron’s recent hiking course, which started at point L, went to point M and then point P, and then returned to point L. What is the measure of LMP formed by Aaron’s hiking course?

A 101°B 79°C 54°D 43°

47°

79°

_____?

Board Answer

Transformations Tessellations and Fractals 300The first 4 stages of a certain fractal are shown below.In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain?

F 243G 54H 81J 27

Board

Transformations Tessellations and Fractals 300

F 243G 54H 81J 27 1 3 9 27

5th Stage? _____

The first 4 stages of a certain fractal are shown below.In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain?

F G

H J

Board Answer


49

Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration.

Step 1: Divide the square into a 3-by-3 grid of squaresStep 2: Shade only the center square of this 3-by-3 grid

What fraction of the 1-unit-by-1-unit square is shaded after the second iteration?

1781

79

6473

Board


F G

H J

49

Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration.

Step 1: Divide the square into a 3-by-3 grid of squaresStep 2: Shade only the center square of this 3-by-3 grid

What fraction of the 1-unit-by-1-unit square is shaded after the second iteration?

1781

79

6473

Board Answer

Transformations Tessellations and Fractals 500The regular octagon below shows selected positions on a combination lock. The dial of the lock is turned 90° clockwise and then 45° counterclockwise. Which pair of points can describe the starting and ending points of a marker on the dial of this lock?A T to UB S to VC W to VD Z to W

Board

Transformations Tessellations and Fractals 500The regular octagon below shows selected positions on a combination lock. The dial of the lock is turned 90° clockwise and then 45° counterclockwise. Which pair of points can describe the starting and ending points of a marker on the dial of this lock?A T to UB S to VC W to VD Z to W 90°

clockwise45° ccwTry: A T to U

A 30(n + 1) B

C 30(n − 1)

D

Board Answer

Geometric Properties 100

360(n - 2)n

The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon with n sides?

360n

Board


A 30(n + 1) B

C 30(n − 1)

D

360(n - 2)n

The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon with n sides?

360n

# Sides Degrees

3 120

4 90

6 60

( )( )

✘✘

Board Answer

Geometric Properties 200On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island formed by the intersections of four streets shown below.What are the measures of the three angles of the garden? 1st Ave

2nd Ave

On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island formed by the intersections of four streets shown below.What are the measures of the three angles of the garden?

Board


1st Ave

2nd Ave

F 90°, 65°, 25°G 90°, 50°, 40°H 90°, 60°, 30°J 130°, 40°, 10° 40°

90°50°

Straight angle = ______180°50°

Board Answer

Geometric Properties 300The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain?F 2nG 2n

H 2n − 1J 2n − 1

Board

Geometric Properties 300The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain?F 2nG 2n

H 2n − 1J 2n − 1

Stage Circles

1 12 33 7

Board Answer


A n − 3

B

C

D n(n − 3)

n - 32

n(n - 3)2

Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides.

Board

Geometric Properties 400Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides.

A n − 3

B

C

D n(n − 3)

n - 32

n(n - 3)2

Board Answer

Geometric Properties 500In the figure shown below, BC is parallel to ED, and AE is perpendicular to ED. The measure of ABC is 130°.What is the measure of BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

In the figure shown below, BC is parallel to ED, and AE is perpendicular to ED. The measure of ABC is 130°.What is the measure of BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Board


130°

There are 3 triangle in the figure

3(180°) = 540°

90°

90°90°

140°

1 4 0

Board Answer

Special Right Triangles 100A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden.

A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden.

Board

Special Right Triangles 100

F 12 ftG 17 ftH 21 ftJ 24 ft

Length of each side = ______12 ft

The length of the diagonal is _____ ft

12 ft12 ft

a2 + b2 = c2

122 + 122 = c2

144 + 144 = c2

288 = c2

16.97 = c

Board Answer

Special Right Triangles 200A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is the kite?

Board

Special Right Triangles 200A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is the kite?

F 110 ftG 127 ftH 156 ftJ 311 ft

220 ft

The height of the kite is _____ ft

a2 + b2 = c2

a2 + b2 = 2202

a2 + a2 = 2202

2a2 = 484002 2a2 = 24200

Board Answer


A 20 mmB 20 mmC 60 mmD 40 mm

3

3

WY∆WXY is a right triangle. Find the length of


Board

Special Right Triangles 300WY∆WXY is a right triangle. Find the length of

3

3

m Y = ____30°30°

60°

80 m

m 80 mm

80 mm

Board

Special Right Triangles 300WY∆WXY is a right triangle. Find the length of


3

3

m Y = ____30°30°

60°

80 m

m 80 mm

80 mm

a2 + b2 = c2

402 + b2 = 802

1600 + b2 = 6400-1600 -1600

b2 = 4800b = 69.282

Board Answer

Special Right Triangles 400The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out?

F 1.7 ftG 18 ftH 10.4 ftJ 6 ft

Board


60°

60°

12 ft6 ft

12 ft

F 1.7 ftG 18 ftH 10.4 ftJ 6 ft

Board


60°

60°

12 ft6 ft

12 ft

Board Answer

Special Right Triangles 500Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be?

Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be?

Board


A 13.4 in.B 10.4 in.C 8.5 in.D 5.2 in.

12 ft

12 ft

12 ft

6 fta2 + b2 = c2

62 + b2 = 122

36 + b2 = 144-36 -36

b2 = 108b = 10.392

Board Answer

Transformations on a Grid 100Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down

Board

Transformations on a Grid 100Find the coordinates of the vertices of the rectangle if it is translated 3 units right and 3 units down

(3,0) (9,0)

(9,2)(3,2)

Board Answer

Transformations on a Grid 200Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a single reflection of the other across the x-axis?A KLM PNMB KRM PQMC KRM PNMD KLM KRM

Board

Transformations on a Grid 200Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a single reflection of the other across the x-axis?A KLM PNMB KRM PQMC KRM PNMD KLM KRM

Board Answer

Transformations on a Grid 300Which pair of the following polygons is congruent?F Polygon A and CG Polygon B and DH Polygon A and BJ Polygon B and C

Board

Transformations on a Grid 300Which pair of the following polygons is congruent?F Polygon A and CG Polygon B and DH Polygon A and BJ Polygon B and C

3

2.5

3

4

Board Answer

Transformations on a Grid 400Figure MNPQ is shown on the coordinate plane.Which transformation creates an image with a vertex at the origin?A Rotate figure MNPQ

90° around MB Reflect figure MNPQ

across the line x = 1C Reflect figure MNPQ

across the line y = 2.5D Translate figure MNPQ

to the left 6 and down 5

Figure MNPQ is shown on the coordinate plane.Which transformation creates an image with a vertex at the origin?A Rotate figure MNPQ

90° around MB Reflect figure MNPQ

across the line x = 1C Reflect figure MNPQ

across the line y = 2.5D Translate figure MNPQ

to the left 6 and down 5

Board

Transformations on a Grid 400

(6, 5)

Board Answer

Transformations on a Grid 500Which coordinates are the vertices of a triangle congruent to ∆MNP?

F (−11, 13), (−9, 16), (−4, 16)G (−8, 5), (−5, 2), (−1, 4)H (−20, 4), (−17, 7), (−12, 5)J (−15, 14), (−18, 17), (−17, 22)

Board

Transformations on a Grid 500Which coordinates are the vertices of a triangle congruent to ∆MNP?

F (−11, 13), (−9, 16), (−4, 16)G (−8, 5), (−5, 2), (−1, 4)H (−20, 4), (−17, 7), (−12, 5)J (−15, 14), (−18, 17), (−17, 22)

Final Jeopardy Category

Board

Final Jeopardy Question

Answer

In the figure below, what is the length of ML in centimeters?

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Board

Final Jeopardy AnswerIn the figure below, what is the length of ML in centimeters?35 cm 28 cm

a2 + b2 = c2

282 + b2 = 352

784 + b2 = 1225-784 -784

b2 = 441b = 21

28 cm100 cm

21 cm

a2 + b2 = c2

282 + b2 = 1002

784 + b2 = 10000-784 -784

b2 = 9216b = 9696 cm

ML = 21 + 96 = 117 cm

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