Solve the following problems: ABCD - trapezoid Is △AOD ∼ △BOC ? Why ? Is △AOB ∼ △COD ? Why ?

Question

Solve the following problems:

ABCD - trapezoid

Is △AOD ∼ △BOC ? Why ?

Is △AOB ∼ △COD ? Why ?

Answer 1

triangle AOB is similar to triangle COD because...

AB is parallel to DC

DB and AC are transversals

∠ABO is congruent to ∠CDO because they are alternate interior angles

∠BAO is congruent to ∠OCD because they are alternate interior angles

usually a transversal that cuts two parallel lines form two pairs of congruent angles but not here because of the segments AD and BC which are preventing this

finally, ∠AOB is congruent to ∠DOC because these angles are vertical angles

so, if you have three pairs of congruent angles you have similar triangles

the other two triangles are not similar

Answer 2

The answer, in general, is No; not unless the trapezoid is isosceles.