Theorem Of Parallelograms

Theorem 1

A diagonal of a parallelogram divides it into two congruent triangles.

Theorem 1

A diagonal of a parallelogram divides it into two congruent triangles.


Given.
A parallelogram ABCD and diagonal AC divides it into two triangles △ABC and △CDA.

To prove. △ABC△CDA

Proof.
Statements
Reasons
In△ABC and △CDA
1. ∠BAC=∠ACD 1.Alt.∠s,AB∠DC and AC is transversal.
2.∠BCA=∠CAD 2. Alternate ∠s, BC∠AD and AC is transversal.
3. AC=CA
3. Common
4.△ABC≌△CDA 4. ASA congruency rule