Diagonal of a Parallelogram Divides it into Two Congruent Triangles
Diagonal of a Parallelogram Divides it into Two Congruent Triangles
Diagonals of a Parallelogram: We know that parallelogram is a quadrilateral in which both the opposite pair of sides are parallel and equal to each other. The 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.
To prove A diagonal, say, AC, of parallelogram ABCD divides it into congruent triangles ABC and CDA i.e. ABC
CDA
Construction Join AC. Proof Since ABCD is a parallelogram. Therefore, AB Now, AD
Again, AB <BAC = <DCA ....(ii) [ Alternate interior angles ] Now, in <BCA = <DAC [From (i)] AC = AC [ Common side ] <BAC = <DCA [ From (i)] So, by ASA congruence criterion, we have |
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| ILLUSTRATION: Find the value of x and y in the figure | |
Solution: In the figure ABCD is a parallelogram and AC is the diagonal. We know that the diagonal of a parallelogram divides it into two congruent triangles Similarly |  |
In the following figure, Diagonal AC divides the inner parallelogram into which two congruent triangles?
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| Right Option : C | |||
| View Explanation | |||
In the following figure, The diagonal divides parallelogram into which congruent triangles
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| Right Option : D | |||
| View Explanation | |||
In the following figure, ABCD is a parallelogram. The diagonal AC divides this parallelogram into which congruent triangles?
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| Right Option : B | |||
| View Explanation | |||
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