On one side of corner A there are segments AB = 5cm and AC = 16cm. On the other side of the same corner, the segments AD 8cm and AE = 10 cm are laid down. Are the triangles ACD and ABE similar?
Triangles ACD and ABE have a common angle.
The length of the segment AB of the triangle ABE is 5 cm, and the length of the segment AD of the triangle ACD is 8 cm.
AB / AD = 5/8.
The length of the segment AE of the triangle ABE is 10 cm, and the length of the segment AC of the triangle ACD is 16 cm.
AE / AC = 10/16 = 5/8.
Since the ratio AB / AD = AE / AC, the sides of the triangles are proportional, and then the triangles ACD and ABE are similar in two proportional sides and the angle between them, which was required to be proved.
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