Question

In Quadrilateral ABCD, AB = 41, BC = 21, CD = 39, DA = 41 and
AC = 50. P is the foot of altitude from A on
ray CB . Q is the
foot of altitude from A on CD. Show that ∠ABC and ∠ADC are
supplementary angles.

Answer 1

Answer:

Since diagonal AC bisects the angles ∠A and ∠C,

we have ∠BAC=∠DAC and ∠BCA=∠DCA.

In triangles ABC and ADC,

we have

∠BAC=∠DAC (given);

∠BCA=∠DCA (given);

AC = AC (common side).

So, by ASA postulate, we have

△BAC≅△DAC

⇒ BA = AD and CB = CD (Corresponding parts of congruent triangle).

hope it's helpful for you ✌️✌️

drop some thanks for my answer