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Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation

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Index card activity Cut an index card diagonally. Here is the shape you will have. [You actually have TWO of these triangles. Save one of them for later!]

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Index card activity Draw an altitude from the right angle to the hypotenuse (you dont need to use a protractor)

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Index card activity How many triangles do you see?

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Index card activity Cut along the altitude to split the big triangle into two smaller right triangles.

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Index card activity You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle). What do you notice about these three triangles?

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Index card activity You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle). What do you notice about these three triangles? They are all SIMILAR to each other!

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Parts of a right triangle

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Here is an altitude from the right angle to the hypotenuse.

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Parts of a right triangle Here is an altitude from the right angle to the hypotenuse.

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Parts of a right triangle For our proportions, alt = altitude and hyp = all of the hypotenuse

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Parts of a right triangle = part of the hypotenuse next to

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Altitude proportion

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Leg 1 proportion

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Leg 2 proportion

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Summary of proportions

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Solve for x Does solving for x involve an altitude?

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Solve for x Yes – x is an altitude

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Solve for x Yes – x is an altitude

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Solve for x Yes – x is an altitude

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Solve for x Yes – x is an altitude

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Solve for y Does solving for y involve an altitude?

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Solve for y No – y is

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Solve for y y is

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Solve for y y is

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Solve for y y is

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Solve for z Does solving for z involve an altitude?

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Solve for z No – z is

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Solve for z z is

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Solve for z z is

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Solve for z z is

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Use Similar Right Triangles. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed.

Use Similar Right Triangles. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed.

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