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Dilation
Similar Figures
Brain Twister
100
Use the diagram below. Let there be a dilation from center O with scale factor r=3. Then, Dilation(P)=P'. In the diagram below, |OP|=5 cm. What is |OP'|? Show your work. Lesson 1 ET
What is 15 cm?
100
Triangle DEF has been dilated from center O by scale factor r=1/2. The dilated triangle is noted by D'E'F'. We also have a triangle D''EF, which is congruent to triangle DEF (i.e., DEF ~= D''EF). Describe the sequence of a dilation followed by a congruence (of one or more rigid motions) that would map triangle D'E'F' onto triangle D''EF. Lesson 8 ET
Triangle D'E'F' needs to be dilated from center O by scale factor r=2 to bring it to the same size as triangle DEF. This produces the triangle noted by DEF. Next, triangle DEF needs to be reflected across line EF. The dilation followed by the reflection maps triangles D'E'F' onto triangle D''EF.
100
Find three positive whole numbers that have the same answer when added together or when multiplied together.
1,2,3
200
Create a rectangle with points (4,5),(5,5),(4,3),(5,3). Dilate from center (0,0) by a scale factor r=.5
What is (2,3), (3,3), (2,1.5), (3,1.5)
200
1) Which two triangles, if any, have similarity that is symmetric? 2) Which three triangles, if any, have similarity that is transitive? Lesson 9 ET
1) S~R and R~S S~T and T~S T~R and R~T 2) One possible solution: Since S~R and R~T, then S~T
200
1. A number has 3 digits and is odd 2. Two digits are the same 3. The sum of the digits in the tens and ones places is odd 4. The sum of the digits is 4 What is the number?
121
300
You are given center O and ray OA. Point A is dilated by a scale factor r= 6/4. Use what you know about FTS to find the location of point A'. Lesson 5 ET
What is the y-coorinate of A' is 6. The x-coorinate is equal to the length of segment A'B'. Since /A'B'/ = r/AB/, then /A'B'/ = 6/4 x 3 = 18/4 = 4/5. The location of A' is (4.5,6).
300
Are the triangles similar? Present an informal argument as to why they are or are not similar. Lesson 10 ET
Yes, they have two pairs of corresponding angles that are equal. You have to use the triangle sum theorem to find the answer.
300
Sixteen red socks and sixteen blue socks are mixed up in a dresser drawer. The socks are all identical except for their color. Suppose Richard wants two matching socks but there is a black out so the room is dark and he can?t see. What is the smallest number of socks that Richard must take out of the drawer to guarantee he has a pair of socks that match?
Suppose the first sock Richard takes out is red. Then, the second sock he takes out is red or blue. If it is red, then he is done. If it is blue, Richard now has 2 socks (one red and one blue). The third sock Richard takes out is red or blue. If it is red, then he has a match with the first sock. If it is blue, he has a match with the second sock. So, Richard needed 3 socks to get a matching pair. This is the same outcome if the first sock Richard had chosen was blue. Thus, 3 socks is the smallest number of socks Richard must take out.
400
The point A(7,4) is dilated from the origin by a scale factor r=3. What are the coordinates of point A'? Lesson 6 ET
A'(21,12)
400
In the diagram below, you have △ABC and △A'B'C'. Based on the information given, is △ABC~△A'B'C'? Explain. Lesson 11 ET
Since there is only information about one pair of corresponding angles, we need to check to see if corresponding sides have equal ratios. That is, does |AB|/|A'B'| =|AC|/|A'C'|, or does (3.5)/(8.75)=6/21? The products are not equal; 73.5≠52.5. Since the corresponding sides do not have equal ratios, the triangles are not similar.
400
There are three people at the dinner table. Two are mothers, and two are daughters. How is this possible?
The women at the table are grandmother, mother, and daughter.
500
Dilate ∠ABC with center O and scale factor r=2. Label the dilated angle, ∠A'B'C' Lesson 7 ET
A'(14,2) B'(6,4) C'(10,8)
500
Henry thinks he can figure out how high his kite is while flying it in the park. First, he lets out 150 feet of string and ties the string to a rock on the ground. Then, he moves from the rock until the string touches the top of his head. He stands up straight, forming a right angle with the ground. He wants to find out the distance from the ground to his kite. He draws the following diagram to illustrate what he has done. a. Has Henry done enough work so far to use similar triangles to help measure the height of the kite? Explain. b. Henry knows he is 5 1/2 feet tall. Henry measures the string from the rock to his head and finds it to be 8 feet. Does he have enough information to determine the height of the kite? If so, find the height of the kite. If not, state what other information would be needed.
A) Yes Based on the sketch, Henry found a center of dilation, point A. Henry has marked points so that, when connected, would make parallel lines. So, the triangles are similar by the AA criterion. Corresponding angles of parallel lines are equal in measure, and the measure of ∠BAC is equal to itself. Since there are two pairs of corresponding angles that are equal, then △BAC~△DAE. B) Yes, there is enough information. Let x represent the height DE. Then, 8/150=(5.5)/x We are looking for the value of x that makes the fractions equivalent. Therefore, 8x=825, and x=103.125 feet. The height of the kite is approximately 103 feet high in the air.
500
Daniel rode his bicycle at a constant speed. After 40 minutes, he cycled 24 km. How far did he cycle in 30 minutes?
Therefore, Daniel cycled 0.6 × 30 = 18 km in 30 minutes.