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By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed
C
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Corresponding angles are congruent
AND Corresponding sides
are proportional in length
Minimum Conditions:1. AA2. SAS3. SSS
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ActivityTake 10 minutes.Use graph paperDraw a right triangleDraw the altitude from the right angleProve that 3 similar triangles are formed
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Activity 1: Birds of a feather stick together! Problem: Mother Nature Enraged!
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The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.
leg
projection
leg
projection
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Using the lengths of the corresponding sides of the triangles formed, we can determine the ratios and from this determine certain geometric properties
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Information we have or need:1. Measurement of leg2. Measurement of projection3. Measurement of hypotenuse
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projection leg
leg hypotenuse
leg
proj
leg
proj
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projection leg
leg hypotenuse
leg
proj
leg
proj
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In a right triangle the length of the leg of a right triangle is the geometric mean between the length of its projection on the hypotenuse
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Worksheet hand out on Property 1
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Information we have or need:1. Altitude2. 2 segments that determine hypotenuse
i.e. projections
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projection altitude
altitude projection
proj proj
altitude
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In a right triangle the length of the altitude drawn from the right angle is the geometric mean of the length of the two segments that determine the hypotenuse
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Worksheet on Property 2
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Information we have or need:1. Hypotenuse2. Altitude3. Length of legs
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hypotenuse altitude leg leg
leg leg
hypotenuse
altitude
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In a right triangle, the product of the length of the hypotenuse and its corresponding altitude is equal to the product of the lengths of the legs.
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Hand out on property 3
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Pythagorean Theorem
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Visions page 182, numbers 1,2,3,4
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Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
or
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The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.