Which statement is true?

A. The altitude drawn to the leg of a right triangle forms two triangles that are similar to each other and to the given triangle.
B. The altitude drawn to the hypotenuse 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.

Multiple post. See my answer posted elsewhere

The altitude drawn to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the given triangle.

To determine which statement is true, let's break down each option:

A. The altitude drawn to the leg of a right triangle forms two triangles that are similar to each other and to the given triangle.

To verify this statement, we can draw a right triangle and construct the altitude from one of the legs. By doing this, we indeed form two smaller triangles that are similar to each other and to the original right triangle. Therefore, option A is true.

B. The altitude drawn to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the given triangle.

Similar to option A, we can draw a right triangle and construct the altitude from the hypotenuse. However, in this case, we do not obtain two similar triangles with the original right triangle. Therefore, option B is false.

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.

A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. In a right triangle, the hypotenuse is not typically divided into equal segments, so constructing a midsegment would not result in two similar triangles. Therefore, option C is false.

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.

For an equilateral triangle, all sides are equal, and the altitude drawn to the hypotenuse would divide it into two congruent triangles. However, in an equilateral triangle, there are not two distinct triangles formed. Therefore, option D is false.

In conclusion, the only correct statement is A. The altitude drawn to the leg of a right triangle forms two triangles that are similar to each other and to the given triangle.