In a right-angled triangle ABC Hypotenuse AB is 10 centimeters Find CD if point D lies on hypotenuse

In a right-angled triangle ABC Hypotenuse AB is 10 centimeters Find CD if point D lies on hypotenuse AB and BC is equal to CD.

Since CD is equal to BD, then the BCD triangle is isosceles, let’s draw the height DH, which will also be the median of the BCD triangle.

Since the angle ACB is straight and DH is perpendicular to BC, the straight lines AC and DH are parallel.

Then DH divides the side BC in half and is parallel to AC, therefore, DH is the middle line of the triangle ABC, which means point D divides the hypotenuse AB in half, AD = BD = 10/2 = 5 cm.

Then CD = BD = 5 cm.

Answer: The length of the CD segment is 5 cm.