In a quadrilateral abcd, the diagonals intersect at point t. thomas has used the alternate interior angles theorem to show that angle adb is congruent to angle dbc and that angle dba is congruent to bdc.
which of the following can thomas use prove that side ab is equal to side dc? (5 points)

solution:

in quadrilateral a b c d

point of intersection of diagonals is point t.

if, ab ║cd

then bd being a transversal and using alternate interior angles theorem gives

∠adb≅∠dbc

∠dba≅∠bdc

to prove, ab = dc,

if this quadrilateral is a parallelogram or rhombus or square or rectangle

ab= cd →[opposite sides of quadrilateral]

the quadrilateral can be any of the four i.e a parallelogram or rhombus or square or rectangle .