Theorem Of Parallelograms

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

▆

---