In parallelogram ABCD, the diagonal AC is the bisector of angle A. Find the perimeter of ABCD if side Ab is side 8.
| January 28, 2021 | education
The angle of the BCA is equal to the angle DАС (internal criss-crossing angles with parallel АD and ВС and secant АС). The angle CAD is equal to the angle CAB (since A is the bisector).
This means that triangle ABC is isosceles (an isosceles triangle has equal angles at the base). Hence, ВA = BC = 8.
In a parallelogram, opposite sides are equal, which means that all sides of the parallelogram are 8, PABCD = 8 * 4 = 32.
Answer: the perimeter of the parallelogram ABCD is 32.
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