By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C
Corresponding angles are congruent AND Corresponding sides are proportional in length Minimum Conditions: 1. AA 2. SAS 3. SSS
Activity Take 10 minutes. Use graph paper Draw a right triangle Draw the altitude from the right angle Prove that 3 similar triangles are formed
Activity 1: Birds of a feather stick together! Problem: Mother Nature Enraged!
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
Using the lengths of the corresponding sides of the triangles formed, we can determine the ratios and from this determine certain geometric properties
Information we have or need: 1. Measurement of leg 2. Measurement of projection 3. Measurement of hypotenuse
leg proj leg proj
leg proj leg proj
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
Worksheet hand out on Property 1
Information we have or need: 1. Altitude 2. 2 segments that determine hypotenuse i.e. projections
proj altitude
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
Worksheet on Property 2
Information we have or need: 1. Hypotenuse 2. Altitude 3. Length of legs
leg hypotenuse altitude
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.
Hand out on property 3
Pythagorean Theorem
Visions page 182, numbers 1,2,3,4
Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. or
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.