Question

Which of the following statements is true?
A) The altitude drawn to the hypotenuse of a right triangle forms two triangles that are similar to
each other and to the given triangle.
B) The altitude drawn to the leg of a right triangle forms two triangles that are similar to each other
and to the given triangle.
C) The midsegment drawn to the hypotenuse of a right triangle forms two triangles that are similar
to each other and to the given triangle.
D) The altitude drawn to the hypotenuse of an equilateral triangle forms two triangles that are
similar to each other and to the given triangle.

Answer 1

A is true. Sketch a 45-45-90 triangle and draw the altitude from the right angle to the hypotenuse. This results in two equal right angled triangles which are also 45-45-90 by the definition of an altitude and the angle bisecter. By the Aaa conjecture the resulting triangles are similar to each other and the original triangle.

Answer 2

Thank you