IM Geo.3.16 Lesson: Bank Shot
What do you notice? What do you wonder?
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[/img]
You need to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the solid orange 5 ball into the upper right corner pocket.
A true bank shot will create two similar right triangles. Determine the measures of the triangles you drew. Are they similar?[br]
Calculate the exact point on the bottom side to aim for and then precisely draw the path of the ball.
How would you hit the ball so that it will end in the hole after one stroke?
Use mirrors to measure the height of a tall object. Label this image with the measurements you made.
Calculate the unknown height.
What if you don’t have a mirror when you’re trying to measure the height of something too tall to measure directly?
[size=150]Brainstorm as many methods other than the mirror method as you can.[/size][br][br]Add to your brainstorm by:[br][list][*]Imagining you have access to any tool you can think of.[/*][*]Imagining you only had a piece of scrap paper and pencil with you. [/*][/list]Pick a method you would like to try, and use it to measure the height of the object your teacher assigns you.
IM Geo.3.16 Practice: Bank Shot
Lin is playing hand ball and wants the ball to bounce off wall CB and land at D.
Where on the wall should she aim if she's standing at point [math]A[/math]?
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.
How can you check to see if your bank shot works?
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! How is Mai so accurate?
What is the height, [math]h[/math], of the student?
In the right triangles shown, the measure of angle ABC is the same as the measure of angle EBD.
What is the length of side [math]BD[/math]? [br]
In right triangle [math]ABC[/math], angle [math]C[/math] is a right angle, [math]AB=17[/math], and [math]BC=15[/math]. What is the length of [math]AC[/math]?
What is the length of [math]AC[/math]?
Fill in the blanks to complete the proof of the Pythagorean Theorem:
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[/img][br][br][math]\frac{a}{x}=\frac{c}{a}[/math] can be rewritten as [img]data:image/png;base64,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[/img] and [math]\frac{b}{y}=\frac{c}{b}[/math] can be written as [img]data:image/png;base64,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[/img]. So, [math]a^2+b^2=[/math][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHcAAAAYCAYAAADAm2IFAAACHElEQVRoBe2Zv8tBYRTHn13KZrUbZZIfs5LEYvEHGJSUQciiDBarWZGSUkoxWGwK+QeMkjDJ7/P2PXXvq9R7t1ede5863eeeO32fzz3POc9zFJlkPJ9Pgr1eLzYzyFZmELlYLCiXy5HT6aRQKETNZpPO57N46eLh3m43UkrRarWi4/FIs9mM3wOBAD0eD9GAxcMtlUoMs1Kp6CDD4TD7xuOx7pM4EQ+3XC4zyHQ6rfOLRqPs6/V6uk/iRDxcFFCTyYS22y3zOxwOZLPZyOFw0Ol0kshU1yQerqZUq5Kz2SxHbb1e5+pZ+y7xqZCTzDBSqRQFg0EGOxqN6H6/i5et5vO5eJEQiDMutuR2u82A4/G4VS1LJF+tVhlwIpEQvTUr5CLJA2dZRO376Pf7DNflconenhVykdQBqLjAgG02G13mYDBgn91ulw1XcmGx2+10uO8XFo1Gg/0+n0903hV9FELkZjIZcrvdtFwueXvGz4xci2h+B66HtZBJq9Ui0XDBCTm3VquRx+Mhr9fLzYNIJELT6VR0d8gUcAEYRSMgo3mw3+8/CiwhwfohQ3zkfig2kcOCKxg2w0XPc71eGxqqzE6nQ91u17IvrAFu14bDoSEnsOQ+Nn5cTIrFIhUKhT8tFotRMpkkPC37/zXw+/2E1qURp3w+/wtX65gYPS+XC8Gu16tlX1gDbf2NOGnfrZwrPecK1mdqaVbkCsb/A0AqlHI92r04AAAAAElFTkSuQmCC[/img]. By factoring, [math]a^2+b^2=[/math][img]data:image/png;base64,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[/img] . We know that [math]x+y=[/math][img]data:image/png;base64,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[/img]. So, [math]a^2+b^2=[/math][img]data:image/png;base64,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[/img].
Match each vocabulary term with its definition.
Clare and Diego are discussing the quadrilaterals.
[size=150]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. [/size][br][br]Do you agree with either of them? Explain your reasoning. [br]