Transcript Transformations, Geometric Properties, Special Right Triangles

Let’s Get Ready
To Play Some . . .
JEOPARDY
JEOPARDY
JEOPARDY
Jeopardy Board
Final Jeopardy
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
Transformations Tessellations and Fractals 100
The 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 100
The 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 200
The 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
B
C
D
101°
79°
54°
43°
Board
Answer
Transformations Tessellations and Fractals 200
The 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
B
C
D
101°
79°
54°
43°
Board
79°
47°
_____?
Transformations Tessellations and Fractals 300
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
243
54
81
27
Board
Answer
Transformations Tessellations and Fractals 300
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
243
54
81
27
Board
1
3
9
27
5th Stage? _____
Transformations Tessellations and Fractals 400
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 squares
Step 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?
F
4
9
H
64
73
Board
G
17
81
J
7
9
Answer
Transformations Tessellations and Fractals 400
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 squares
Step 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?
F
4
9
H
64
73
Board
G
17
81
J
7
9
Transformations Tessellations and Fractals 500
The 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
B
C
D
T to U
S to V
W to V
Z to W
Board
Answer
Transformations Tessellations and Fractals 500
The 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
B
C
D
T to U
S to V
W to V
Z to W
Try:
Board
A T to U
90°
clockwise
Geometric Properties 100
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?
A 30(n + 1)
360
B (n - 2)n
C 30(n − 1)
D
360
n
Board
Answer
Geometric Properties 100
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?
A 30(n + 1)
✘
( 360 )
B ((n - 2)n)
✘
C 30(n − 1)
D
360
n
Board
# Sides
Degrees
3
120
4
90
6
60
Geometric Properties 200
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?
1st Ave
2nd Ave
Board
Answer
Geometric Properties 200
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?
F
G
H
J
90°, 65°, 25°
90°, 50°, 40°
90°, 60°, 30°
130°, 40°, 10°
Board
Straight angle = ______
180°
50°
1st Ave
50°
90°
40°
2nd Ave
Geometric Properties 300
The figure below shows the first 3 stages of a
fractal. How many circles will the nth stage of
this fractal contain?
F
G
H
J
2n
2n
2n − 1
2n − 1
Board
Answer
Geometric Properties 300
The figure below shows the first 3 stages of a
fractal. How many circles will the nth stage of
this fractal contain?
F
G
H
J
2n
2n
2n − 1
2n − 1
Stage
Board
1
2
3
Circles
1
3
7
Geometric Properties 400
Use the table to determine the expression that
best represents the number of diagonals of
any convex polygon having n sides.
A
n−3
B
n-3
2
n(n - 3)
2
C
D
n(n − 3)
Board
Answer
Geometric Properties 400
Use the table to determine the expression that
best represents the number of diagonals of
any convex polygon having n sides.
A
n−3
B
n-3
2
n(n - 3)
2
C
D
n(n − 3)
Board
Geometric Properties 500
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
Answer
Geometric Properties 500
In the figure shown below, BC is parallel to
ED, and AE is perpendicular to ED. The
130°
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
There
are 3
triangle
in the
figure
3(180°)
= 540°
1 4 0
90°
140°
90°
90°
Special Right Triangles 100
A fence around a square garden has a
perimeter of 48 feet. Find the approximate
length of the diagonal of this square garden.
Board
Answer
Special Right Triangles 100
A fence around a square garden has a
perimeter of 48 feet. Find the approximate
length of the diagonal of this square garden.
The length of the diagonal is _____ ft
F 12 ft
G 17 ft
H 21 ft
J
24 ft
12 ft
Length of each side = ______
Board
a2 + b2 = c2
122 + 122 = c2
144 + 144 = c2
288 = c2
16.97 = c
Special Right Triangles 200
A 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
Answer
Special Right Triangles 200
A kite string is 220
feet long from the kite to
220 ft
the ground. The string makes a 45° angle
with the ground. About how high off the
ground is the kite?
F
G
H
J
110 ft
127 ft
156 ft
311 ft
a2 + b2 = c2
a2 + b2 = 2202
a2 + a2 = 2202
2a2 = 48400
2
2
2
a = 24200
The height of the kite is _____ ft
Board
Special Right Triangles 300
∆WXY is a right triangle. Find the length of WY
A
B
C
D
20 mm
20 3 mm
60 mm
40 3 mm
Board
Answer
Special Right Triangles 300
∆WXY is a right triangle. Find the length of WY
A
B
C
D
20 mm
20 3 mm
60 mm
40 3 mm
60°
30°
m Y = ____
30°
80 mm
Board
Special Right Triangles 300
∆WXY is a right triangle. Find the length of WY
A
B
C
D
20 mm
20 3 mm
60 mm
40 3 mm
a2 + b 2 = c 2
402 + b2 = 802
1600 + b2 = 6400
-1600
-1600
b2 = 4800
b = 69.282
Board
60°
30°
m Y = ____
30°
80 mm
Special Right Triangles 400
The 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?
Board
Answer
Special Right Triangles 400
The 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 ft
60°
G 18 ft
6 ft
12 ft
H 10.4 ft
J
6 ft
60°
Board
Special Right Triangles 400
The 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 ft
60°
G 18 ft
6 ft
12 ft
H 10.4 ft
J
6 ft
60°
Board
Special Right Triangles 500
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
Answer
Special Right Triangles 500
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?
A
B
C
D
13.4 in.
10.4 in.
8.5 in.
5.2 in.
Board
12 ft
a2 + b2 = c 2
62 + b2 = 122
36 + b2 = 144
-36
-36
b2 = 108
b = 10.392
12 ft
6 ft
12 ft
Transformations on a Grid 100
Find the coordinates of the vertices of the
rectangle if it is translated 3 units right and 3
units down
Board
Answer
Transformations on a Grid 100
Find the coordinates of the vertices of the
rectangle if it is translated 3 units right and 3
units down
(3,2)
(3,0)
Board
(9,2)
(9,0)
Transformations on a Grid 200
Look 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  PNM
B KRM  PQM
C KRM  PNM
D KLM  KRM
Board
Answer
Transformations on a Grid 200
Look 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  PNM
B KRM  PQM
C KRM  PNM
D KLM  KRM
Board
Transformations on a Grid 300
Which pair of the following polygons is congruent?
F Polygon A and C
G Polygon B and D
H Polygon A and B
J Polygon B and C
Board
Answer
Transformations on a Grid 300
Which pair of the following polygons is congruent?
F Polygon A and C
G Polygon B and D
H Polygon A and B
2.5
J Polygon B and C
3
4
3
Board
Transformations on a Grid 400
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 M
B Reflect figure MNPQ
across the line x = 1
C Reflect figure MNPQ
across the line y = 2.5
D Translate figure MNPQ
to the left 6 and down 5
Board
Answer
Transformations on a Grid 400
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 M
B Reflect figure MNPQ
across the line x = 1
C Reflect figure MNPQ
across the line y = 2.5
D Translate figure MNPQ
to the left 6 and down 5
Board
(6, 5)
Transformations on a Grid 500
Which coordinates are the vertices of a
triangle congruent to ∆MNP?
F
G
H
J
(−11, 13), (−9, 16), (−4, 16)
(−8, 5), (−5, 2), (−1, 4)
(−20, 4), (−17, 7), (−12, 5)
(−15, 14), (−18, 17), (−17, 22)
Board
Answer
Transformations on a Grid 500
Which coordinates are the vertices of a
triangle congruent to ∆MNP?
F
G
H
J
(−11, 13), (−9, 16), (−4, 16)
(−8, 5), (−5, 2), (−1, 4)
(−20, 4), (−17, 7), (−12, 5)
(−15, 14), (−18, 17), (−17, 22)
Board
Final Jeopardy Category
Board
Final Jeopardy Question
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.
Answer
Final Jeopardy Answer
In the figure below, what is the length of ML
in centimeters?
35 cm
ML = 21 + 96 = 117 cm
28 cm
a2 + b2 = c2
282 + b2 = 352
784 + b2 = 1225
-784
-784
b2 = 441
b = 21 cm
28 cm
Board
a2 + b2 = c 2
282 + b2 = 1002
784 + b2 = 10000
-784
-784
b2 = 9216
b = 96 cm
100 cm
1
1
7