Demonstrate & prove Einstein’s Lesser Theorem through measurement and proof.

Visual Proof: Demonstration of Einstein's Lesser Thereom

How does the diagram above demonstrate that the blue and brown triangles are similar to the large triangle and to each other? (Hint: Consider the angles.)

Constructing the Diagram:

1. Toolbar ImageConstruct a circle of any diameter. 2. Toolbar ImageConstruct a diameter using a line through the center and a point on the circumference. 3. Toolbar ImageUsing the ends of the diameter andany other point on the circle, construct a triangle. 4. Toolbar ImageConstruct the altitude of the triangle using the perpendicular line tool. 5. Toolbar ImageLabel the intersection of the altitude and the base using the perpendicular line tool.

Einstien's Lesser Theorem

Einstien's Lesser Theorem
Given a right triangle, an altitude drawn from the right angle to the hypotenuse will form two smaller triangles which are similar to each other and the original triangle.

Observation & Measurement

Measure the following using the measurement tool Toolbar Imageor the Length command. CE by using Length[C,E] AC by using Length[A,C] CB by using Length[C,B] Calculate the product of and record it below. Calculate and record it on your diagram.

Paragraph Proof

Given: EC is the altitude of the right Prove: