Geo-2017-Construction11-SimilarRightTriangles
Objective:
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.
Construct a circle of any diameter.
2.
Construct a diameter using a line through the center and a point on the circumference.
3.
Using the ends of the diameter andany other point on the circle, construct a triangle.
4.
Construct the altitude of the triangle using the perpendicular line tool.
5.
Label the intersection of the altitude and the base using the perpendicular line tool.
![Toolbar Image](/images/ggb/toolbar/mode_circle2.png)
![Toolbar Image](/images/ggb/toolbar/mode_join.png)
![Toolbar Image](/images/ggb/toolbar/mode_polygon.png)
![Toolbar Image](/images/ggb/toolbar/mode_orthogonal.png)
![Toolbar Image](/images/ggb/toolbar/mode_intersect.png)
Einstien's Lesser Theorem
![Einstien's Lesser Theorem](https://beta.geogebra.org/resource/GMT6vmZN/PKyBKsBLmJRfX45q/material-GMT6vmZN.png)
Observation & Measurement
Measure the following using the measurement tool or 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: