Which triangle is similar to triangle AEB using the Pieces of Right Triangles Similarity Theorem? Triangle ABC has measure of angle ABC equal to 90 degrees. E is a point on the hypotenuse AC such that the segment BE is perpendicular to AC. D is a point outside the triangle on the right of E so that triangle EDC has the measure of angle EDC equal to 90 degrees.

Triangle DCE
Triangle ECB
Triangle BEC
Triangle CED

The answer is triangle BEC

Step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.