Special right triangles (LDM)
- Similarity and altitudes in right triangles (CE7)
Sample Solution
Similarity in right triangles can be used to find the altitude of a triangle. Altitudes are lines that extend outwards from one vertex of a triangle and meet the opposite side at a 90-degree angle, forming two congruent triangles. By using similarity in right triangles, we can determine the ratio between the lengths of each leg and hypotenuse in both triangles. This ratio is known as the Pythagorean Theorem, which states that for any right triangle, the sum of squares of its two legs will equal to the square of its hypotenuse.
Using this theorem and properties of similar figures, it is possible to calculate an unknown side length on one triangle when given all three sides for another triangle. To do so, we need to set up an equation with both ratios being equal. Since they are similar figures we know their corresponding angles must also be equal; therefore if we know two sides on one triange we can solve for x as long as we have all three sides in another triangle.