In parallelogram ABCD, the obtuse angle bisector ADC intersects side BC at point E at an angle DEC equal

| April 16, 2021 | education

In parallelogram ABCD, the obtuse angle bisector ADC intersects side BC at point E at an angle DEC equal to 60 degrees and divides the side into segments BE = 3 cm and CE = 4 cm. Find the perimeter of the parallelogram

1. The bisector DE divides the parallelogram into two geometric shapes. One of them, according to the properties of the parallelogram, is the isosceles triangle CED.

2. The angles at its base are equal. ∠СDE = ∠СDE.

3. We calculate their values:

∠СDE = ∠СDE = (180 ° – ∠СОD) / 2 = (180 ° – 60 °) / 2 = 60 °. All angles of the CED triangle are equal to 60 °. Therefore, the indicated triangle is equilateral.

4. Hence, CE = DE = CD = 4 centimeters.

5. Sun = 3 + 4 = 7 centimeters.

6. According to the properties of a parallelogram, the sides opposite each other are equal.

Therefore, AB = CD = 4 centimeters, BC = AD = 7 centimeters.

7. Calculate the perimeter (P) of a given geometric figure:

P = 2 x 4 + 2 x 7 = 22 centimeters.

Answer: The perimeter of a given parallelogram is 22 centimeters.



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