10. HOPE is parallelogram whose opposite sides are equal. Opposite angles are equal and diagonals bisect each other. Adjacent angles of a parallelogram are supplementary.i). In the parallelogram HOPE, find the measure of ZHOP? a. 50° b. 110° c. 120° d. 100° ii). By using the property find the measure of ZPHO? a. 30° b. 50° c. 40° d. 35⁰ iii). What are the measures of ZEPO and y? a. 70°, 30° b. 30°, 70° c. 80°, 40° d. 70°, 40° iv). If the perimeter of HOPE is 160 cm and one of sides is 50 cm. and what are the measures of other sides? a) 30cm, 30cm, 50cm b) 40cm, 30cm, 40cm c) 30cm, 30cm, 60cm d) 40cm, 50cm, 50cm
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Step-by-step explanation:option A is correct
To prove that the opposite angles of a parallelogram are equal.,
Construction: Draw a parallelogram ABCD. Join BD.
Proof: In triangle ABD and BCD
AB = CD [opposite sides of the parallelogram]
BC = DA [opposite sides of the parallelogram]
BD is common
So triangles ABD and BCD are congruent.
Hence <A = <C , sides opposite BD.
Similarly <B = <D.
Therefore, the opposite angles of a parallelogram are equal.
Proved.
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