Lydia has drawn quadrilateral ABCD with diagonal AC . According to her measurements, m∠DAC=m∠BCA and m∠DCA=m∠BAC . Without taking additional measurements, Lydia claims △ABC≅△CDA according to the ASA triangle congruence criteria. Explain why Lydia is correct.

Lydia is correct because the ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent which would prove her statement correct.

Step-by-step explanation:

whats the question?

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.