G.GSRT.5 Geometric Mean
What theorem is being dynamically illustrated in the applet below? (Feel free to move the black point or white points anywhere!)
Theorem:
The altitude drawn to the hypotenuse of a right triangle splits that right triangle into 2 smaller right triangles that are both similar to the original triangle and similar to each other.
(Triangles are similar by AA~ Theorem!)
Remembering the geometric mean relationships can be difficult.
Select the check box "Point A." Notice that the 3 segments in this geometric mean relationship intersect at A. The corresponding segments of the similar triangles that create this relationship are highlighted below.
Select the check box "Point B." Notice that the 3 segments in this geometric mean relationship intersect at B. The corresponding segments of the similar triangles that create this relationship are highlighted below.
Select the check box "Point C." Notice that the 3 segments in this geometric mean relationship intersect at C. The corresponding segments of the similar triangles that create this relationship are highlighted below.
Question 1
Question 2
Question 3
Question 4
Question 5
1) 2) 3) 4) 5)