# Hello friends Prove that the diagonals …

Hello friends Prove that the diagonals of a parallelogram divides it into two congruent triangles

Gaurav Seth 4 weeks ago

Given: ABCD is a parallelogram. AC is a diagonal of parallelogram ABCD which divides it into two triangles, namely, ∆ABC and ∆CDA.

To Prove: ∆ABC ≅ ∆CDA
Proof: BC || DA
| Opposite sides of a parallelogram are parallel
and AC is a transversal
∴ ∠BCA = ∠DAC    ...(1)
| Pair of alternate interior angles
Also, AB || DC
Opposite sides of a parallelogram are parallel
and AC is a transversal
∴ ∠BAC = ∠DCA    ...(2)
| Pair of alternate interior angles
AC = CA    ...(3) | Common
In view of (1), (2) and (3),
∆ABC ≅ ∆CDA
| ASA congruence criterion

Related Questions:

## myCBSEguide

Trusted by 1 Crore+ Students

#### CBSE Test Generator

Create papers in minutes

Print with your name & Logo

3 Lakhs+ Questions

Solutions Included

Based on CBSE Blueprint

Best fit for Schools & Tutors

#### Work from Home

• Work from home with us
• Create questions or review them from home

No software required, no contract to sign. Simply apply as teacher, take eligibility test and start working with us. Required desktop or laptop with internet connection