In parallelogram ABCD, bisector AL of angle A divides side BC into segments BL = 3 cm, LC = 5 cm.

univerkov | April 19, 2021 | education

In parallelogram ABCD, bisector AL of angle A divides side BC into segments BL = 3 cm, LC = 5 cm. a) the perimeter of the parallelogram; b) the length of the midline of the ALCD trapezoid.

1. The bisector AL of the parallelogram ABCD cuts off the triangle ABL from it, which is isosceles (according to the properties of the parallelogram).

Therefore, BL = AB = 3 cm.

2. ВС = АD = ВL + СL = 3 + 5 = 8 cm.

3. Opposite sides of the parallelogram ABCD are equal (according to the parallelogram properties). Therefore, AB = CD = 3 cm. AD = BC = 8 cm.

4. The perimeter of the parallelogram = 2AB + 2AD = 2 x 3 + 2 x 8 = 6 + 16 = 22 cm.

5. The middle line of the trapezoid is АLCD = (АD + СL): 2 = (8 + 5): 2 = 13: 2 = 6.5 cm.

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