The large side of the parallelogram is two of the two roots, and the larger angle between the diagonals

| June 9, 2021 | education

The large side of the parallelogram is two of the two roots, and the larger angle between the diagonals is equal to the larger angle of the parallelogram. Find the big diagonal

According to the condition, the angle ADC = BOC, the angle BCO is equal to the angle OAD as criss-crossing angles at the intersection of parallel straight lines AD and BC secant AC. Then the triangles BOC and ACD are similar in the first sign of similarity of triangles – in two corners.

The opposite sides of the parallelogram are equal, then AD = BC = 2 * √2 cm.

Then AD / OC = AC / BC.

Since AC = 2 * OC then: AD / OC = 2 * OC / BC.

2 * OC ^ 2 = AD * BC = 2 * √2 * 2 * √2 = 8 cm.

OC ^ 2 = 4 cm.

OC = 2 cm, then AC = 2 * OC = 2 * 2 = 4 cm.

Answer: The length of the larger diagonal is 4 cm.



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