Bank Shot

ID: lubul-kagun
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
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21 questions

Bank Shot

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Problem 1

1) Lin is playing hand ball and wants the ball to bounce off wall CBCB and land at DD. Where on the wall should she aim if she's standing at point AA?

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a)

7.8 feet away from point BB

b)

13.3 feet away from point BB

c)

Anywhere along the wall since all of the triangles will be similar

Problem 2

2) You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.

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3) How can you check to see if your bank shot works?

Problem 3

Mai is playing a game with a class of second graders. Mai knows she is exactly 120 inches from the mirror on the floor. She has students stand so that she can just see the top of their heads and then guesses their heights. The students are amazed!

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4) What is the height, hh, of the student?

5) How is Mai so accurate?

Problem 4

6) In the right triangles shown, the measure of angle ABCABC is the same as the measure of angle ​​​​​EBDEBD. What is the length of side BDBD?

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Problem 5

7) In right triangle ABCABC, angle CC is a right angle, AB=17AB = 17, and BC=15BC = 15. What is the length of ACAC?

Problem 6

Complete this proof of the Pythagorean Theorem, using items from the Bank of Expressions and Equations below to fill in the blanks.

ax=ca\frac{a}{x} = \frac{c}{a} can be rewritten as 1\underline{\quad\quad 1 \quad\quad} and by=cb\frac{b}{y} = \frac{c}{b} can be written as 2\underline{\quad\quad 2 \quad\quad}. So, a2+b2=3a^2 + b^2 = \underline{\quad\quad 3 \quad\quad}. By factoring, a2+b2=4a^2 + b^2 = \underline{\quad\quad 4 \quad\quad}. We know that x+y=5x + y = \underline{\quad\quad 5 \quad\quad}. So, a2+b2=6a^2 + b^2 = \underline{\quad\quad 6 \quad\quad}.

Bank of Expressions and Equations: aa, bb, cc, c2c^2, xc+ycxc + yc, a2=xca^2 = xc, (x+y)c(x + y)c, b2=ycb^2 = yc

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8) Blank 1

9) Blank 2

10) Blank 3

11) Blank 4

12) Blank 5

13) Blank 6

Problem 7

14) In right triangle ABCABC, altitude CDCD with length hh is drawn to its hypotenuse. We also know AD=4AD = 4 and DB=16DB = 16. What is the length of ACAC?

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Problem 8

Match each vocabulary term with its definition. Write the number of the corresponding definition in the answer box.

IDDefinitionThere is a sequence of rigid motions and dilations1that takes the first figure onto the second.When 2 angles of one triangle are congruent to 22 angles of a second triangle, the 2 triangleswill be similar.A transformation using a center C and scale factor 3k that takes a point A to another point along the ray CAwhose distance is k times farther from C than A is.A drawing in which all lengths in the drawing 4correspond to lengths in the object by the samescale.A constant multiple by which all lengths of the original 5figure are multiplied\begin{array}{|l|l|} \hline \\[-1em] \textbf{ID} & \textbf{Definition} \\[-1em] \\ \hline \\[-1em] & \text{There is a sequence of rigid motions and dilations} \\ 1 & \text{that takes the first figure onto the second.} \\[-1em] \\ \hline \\[-1em] & \text{When 2 angles of one triangle are congruent to } \\ 2 & \text{2 angles of a second triangle, the 2 triangles}\\ &\text{will be similar.} \\[-1em] \\ \hline \\[-1em] & \text{A transformation using a center } C \text{ and scale factor } \\ 3 & k \text{ that takes a point } A \text { to another point along the ray } CA\\ &\text{whose distance is } k \text{ times farther from } C \text{ than } A \text{ is.} \\[-1em] \\ \hline \\[-1em] & \text{A drawing in which all lengths in the drawing } \\ 4 & \text{correspond to lengths in the object by the same}\\ &\text{scale.} \\[-1em] \\ \hline \\[-1em] & \text{A constant multiple by which all lengths of the original } \\ 5 & \text{figure are multiplied} \\[-1em] \\ \hline \end{array}

15) Scale Drawing

16) Scale Factor

17) Dilation

18) Similar Figures

19) Angle-Angle Similarity Theorem

Problem 9

Clare and Diego are discussing the quadrilaterals. Clare thinks the quadrilaterals are similar because the side lengths are proportional. Diego thinks they need more information to know for sure if they are similar.

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20) Which one is correct?

21) Explain your reasoning.