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Example 1: Show that each angle of a rectangle is a right angle. |
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Answer» Let us consider a rectangle ABCD.We know that the diagonals of a rectangle are equal. Therefore, AC = DBIn triangle ABC and triangle DCB,AB = DC (Opposite sides of a parallelogram)AC = DBBC = CB (Common side)Therefore, triangle ABC is congruent to triangle DCB.And, angle ABC = angle DCB (CPCT)And, angle ABC + angle DCB = 180° (Adjacent angles of a parallelogram are supplementary/Co interior angles)Therefore, angle ABC = angle DCB = 90°And, angle ABC = angle ADC = 90° and angle DCB = angle BAC = 90° (Opposite angles of a parallelogram are equal.)Hence, each angle of a rectangle measures 90°Hence proved. |
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