ABCD is a parallelogram and AC is one of its diagonals (see figure).
What can you say about triangle ABC and triangle CDA? Explain your answers.
[Hint: Opposite sides and opposite angles of a parallelogram are
congruent]
Answers
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Given ABCD is a parallelogram and AC is one of its diagonals
To Find : What can be said about triangle ABC and triangle CDA
Solution:
ABCD is a parallelogram
opposite sides of parallelogram are equal
AB = CD
BC = AD
in ΔABC and ΔCDA
AB = CD
BC = DA
AC = CA Common
=> ΔABC ≅ ΔCDA ( SSS )
As hint is given opposite angles of a parallelogram are
congruent using that
in ΔABC and ΔCDA
AB = CD
∠B = ∠D opposite angles of parallelogram
BC = DA
=> ΔABC ≅ ΔCDA ( SAS )
triangle ABC and triangle CDA are congruent
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