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

Posted by Tidke Pranav 3 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 3 years, 5 months 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

1Thank You

ANSWER

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CBSE > Class 09 > Mathematics