Parallelograms I — O/L Mathematics

How do I practise Parallelograms I?

2 questions with worked solutions

1. In a parallelogram ABCD, angle A = 70°. Find the magnitude of angle B.
   1. A) 90°
   2. B) 140°
   3. C) 70°
   4. D) 110°
   Check my answer

   Correct answer: D) 110°

   In a parallelogram, adjacent (consecutive) interior angles between parallel lines are allied/supplementary (sum to 180°). Therefore, angle B = 180° - 70° = 110°.

   Show worked solution

   Step 1: Identify geometric property: AD is parallel to BC, AB is a transversal. Step 2: Consecutive interior angles are supplementary: angle A + angle B = 180°. Step 3: Solve for angle B: angle B = 180° - 70° = 110°. Answer: 110°.
   Modelled on: the O/L Mathematics examination pattern
2. The diagonals of parallelogram PQRS intersect at O. If PR = 14 cm and QS = 10 cm, find the lengths of PO and QO.
   1. A) PO = 5 cm, QO = 7 cm
   2. B) PO = 14 cm, QO = 10 cm
   3. C) PO = 12 cm, QO = 12 cm
   4. D) PO = 7 cm, QO = 5 cm
   Check my answer

   Correct answer: D) PO = 7 cm, QO = 5 cm

   The diagonals of a parallelogram bisect each other, so O is the midpoint of both PR and QS. Therefore PO = 14 / 2 = 7 cm and QO = 10 / 2 = 5 cm.

   Show worked solution

   Step 1: State the property: the diagonals of a parallelogram bisect each other. Step 2: O is the midpoint of PR: PO = PR / 2 = 14 / 2 = 7 cm. Step 3: O is the midpoint of QS: QO = QS / 2 = 10 / 2 = 5 cm. Answer: PO = 7 cm, QO = 5 cm.
   Modelled on: the O/L Mathematics examination pattern

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Where does Parallelograms I fit in the syllabus?

Grade 10 · Term 2