ABCD is a quadrilateral where AC is a diagonal cutting ABCD into 2 triangles, triangle ABC and triangle CDA - Maths - Congruence of Triangles

Question

ABCD is a quadrilateral where AC is a diagonal cutting ABCD into 2
triangles, triangle ABC and triangle CDA
AB is parallel to DC and AB=DC
(a)Is angle BAC equal to angle DCA?why?
(b) is triangle ABC conguent to triangle CDA?why?
(c) is angle B equal to angle D?why?

Anuradha Sharma · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/14160540139083%20png">
If AB || CD and AB= CD then AD =BC because distance between the
ends points of finite and equal parallel lines is same
So ABCD can be rectangle and square and parallelogram,

∠BAC=∠DCA Alternate interior angle as AB∥CD and AC is transversal

In triangle ABC and DCA, AC=ACAB=CD given∠ACD=∠CAB provedSO △ ABC ≅△DCA by SAS congruency

SInce it can be rectangle, square or parallelogram hence angle B
will be equal to angle D

ABCD is a quadrilateral where AC is a diagonal cutting ABCD into 2 triangles, triangle ABC and triangle CDA.AB is parallel to DC and AB=DC. (a)Is angle BAC equal to angle DCA?why? (b) is triangle ABC conguent to triangle CDA?why? (c) is angle B equal to angle D?why?

ABCD is a quadrilateral where AC is a diagonal cutting ABCD into 2 triangles, triangle ABC and triangle CDA.
AB is parallel to DC and AB=DC.

(a)Is angle BAC equal to angle DCA?why?

(b) is triangle ABC conguent to triangle CDA?why?

(c) is angle B equal to angle D?why?