Search Results for “similar-triangles”
Simple Similar Triangles
Drag points A, B, and C to change the size and shape of the blue triangle, and its white counterpart that is similar (constrained by proportional SAS). Drag the Red point D to change the ratio in sizes. Observe the multitude of calculated output lengths and angles, and how they match the proportion value, proving similarity, regardless of the triangles' shapes/sizes.
Bhaskara’s Proof
This app allows you to explore algebraic proof by the ancient Hindu mathematician Bhaskara, who used the properties of similarity to prove the theorem.
Angle Bisector
The angle bisector of a triangle splits the opposite side in the same ratio as the sides themselves. The proof of this is illustrated.
October Problem
Given two concentric similar (and similarly situated) ellipses, we create the two tangents from a point on the outer ellipse to the inner ellipse. Notice the area of the triangle formed by E and the tangency points F and G is constant as you drag E. Why? You can change the semi major axis lengths a and b, or the scale factor k.
Euclid Book 6 Proposition 31
In right angled triangles, the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle
Euclids Elements – Book 4 – Proposition 11
Can you create a regular pentagon without a protractor? Because it’s pretty impressive how Euclid did it with only a compass and a ruler. Note that the yellow triangle is similar to the one inside the pentagon.
Euclid Book 6 Proposition 8
If in a right-angled triangle a perpendicular is drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another.
