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
D. makes no sense at all. An equilateral triangle has no hypotenuse.
C. is obviously not correct unless the right triangle is 45-45-90.
A. An altitude drawn to a leg of a right triangle would follow one side and not divide the triangle at all
What does that leave you with?
The correct statement is 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.
To determine which statement is true, we need to understand the definitions of altitude, hypotenuse, and midsegment in relation to triangles.
An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side, forming a right angle.
The hypotenuse is the longest side of a right triangle and is opposite the right angle.
A midsegment is a line segment connecting the midpoints of two sides of a triangle.
Now let's analyze each statement:
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. This statement is not true. When an altitude is drawn to the leg of a right triangle, it forms two right triangles, but they are not necessarily similar to each other or to the original 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. This statement is true. When an altitude is drawn to the hypotenuse of a right triangle, it creates two smaller triangles that are similar to each other and to the original 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. This statement is not true. The midsegment of a triangle does not necessarily form two triangles that are similar to each other or to the original 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. This statement is not relevant to the question because it is referring to an equilateral triangle, not a right triangle.
Therefore, the correct answer is 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.
Which is the hypotenuse-leg theorem?
A. If the hypotenuse and one leg of a right triangle are similar to the corresponding parts of another right triangle, then the triangles are congruent. B. If the hypotenuse is congruent to the corresponding part of another right triangle, then the triangles are congruent. C. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are equilateral. D. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.