Similar Figures
A 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it?
4ft
What is the probability of rolling a 4 on a standard six-sided die?
The probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Since there is only one 4 on a six-sided die, the probability is:
P(rolling a 4) = 1/6
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree to the nearest foot
33 feet
ΔCDE was translated down and right to form triangle
ΔC′D′E
Is this a rigid transformation?
yes
Area of a rectangle/ parallelogram
A=bh
A telephone booth that is 8 ft tall casts a shadow that is 4 ft long. Find the height of a lawn ornament that casts a 2 ft shadow.
4ft
What is the probability of drawing a red card from a standard deck of 52 cards?
A standard deck has 26 red cards (13 hearts and 13 diamonds). Therefore, the probability is:
P(drawing a red card) = 26/52 = 1/2
An 8 foot metal guy wire is attached to a broken stop sign to secure its position until repairs can be made. Attached to a stake in the ground, the guy wire makes an angle of 51º with the ground. How far from the foot of the stop sign is the stake, to the nearest tenth of a foot?
5.0 feet
Rectangle ABCD and WXYZ or dilation of each other.
Are they rigid?
No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.
Area of a triangle
A=bh/2
A map has a scale of 3 cm : 18 km. If Riverside and Smithville are 54 km apart then they are how far apart on the map?
9cm
What is the probability of drawing a face card (Jack, Queen, or King) from a standard deck of 52 cards?
There are 12 face cards in total (3 face cards in each of the 4 suits). Therefore, the probability is:
P(drawing a face card) = 12/52 = 3/13
On a windy day, a 90 foot rope tightly secures a hot air balloon to a stake in the ground. From the balloon, the angle of depression of the stake is 62º. Find, to the nearest foot, the height of the balloon, assuming the wind to be constant.
79 feet
ΔXYZ was reflected to form ΔLMN.
Which statements are false regarding the triangle?
ΔXYZ ≅ ΔLMN
∠Y ≅ ∠M
∠X ≅ ∠L
XZ ≅LM
XZ ≅LM
Area of a trapezoid
A=(b1+b2)h/2
Find the distance between Riverside and Milton if they are 12 cm apart on a map with a scale of 4 cm : 21 km.
63km
A bag contains 8 red, 7 blue, and 6 green balls. One ball is picked at random. What is the probability that it is either red or green
The total number of balls is 8 + 7 + 6 = 21. The number of favorable outcomes (red or green) is 8 + 6 = 14. Therefore, the probability is:
P(drawing a red or green ball) = 14/21 = 2/3
From point P on the ground, the angle of elevation of an airplane is 23º. The altitude of the plane is 1200 meters. What is the distance from point P to the airplane, to the nearest tenth of a meter?
3071.1m
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid GHIJ. Write the congruence statement for the trapezoid.
CDEF ≅ GHIJ
Area of a circle
A=3.14r^2
A model house is 12 cm wide. If it was built with a scale of 3 cm : 4 m then how wide is the real house?
16 m
In a litter of mice, 4 are selected at random without replacement. Among these, 2 are white. The probability that both white mice are chosen is twice the probability that neither is chosen. How many mice are there in the litter?
The total number of mice in the litter is 7.
From the hay loft door, Ted sees his dog on the ground. The angle of depression of the dog is 40º. Ted's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Ted (to the nearest foot)?
19 feet
Rectangle ABCD is congruent to rectangle HGJK.
length =18
width =11
What is the area of rectangle ABCD?
198 square inches
Surface area of a rectangular prism
SA=2lw+2lh+2wh