Solving problems involving parallelograms, trapezoids and kites
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This document defines and discusses the properties of parallelograms, trapezoids, and kites. It states that parallelograms have two pairs of parallel sides with opposite sides and angles being congruent. Trapezoids have one pair of parallel sides, and the median is half the sum of the bases. Kites have two pairs of adjacent congruent sides and perpendicular diagonals that bisect angles and sides. Understanding these properties is important for solving geometry problems.
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Solving problems involving parallelograms, trapezoids and kites
- 1. SOLVING PROBLEMS INVOLVING PARALLELOGRAMS, TRAPEZOIDS AND KITES In the previous lessons, we have learned about these three types of quadrilaterals: the parallelogram, the trapezoid, and the kite. We have also learned about each of their properties. It is important that you, as a student on geometry, remember these properties since they are useful in solving problems on geometry.
- 2. Parallelogram • A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. • The properties of a parallelogram are: • The opposite sides are congruent. • The opposite angles are congruent. • The non-opposite angles are supplementary angles. • The diagonals bisect each other. • Each diagonal divides a parallelogram into two congruent triangles.
- 3. Trapezoid • A trapezoid is a quadrilateral with exactly one pair of parallel sides, while an isosceles trapezoid is a trapezoid with congruent non-parallel sides. • The median of a trapezoid is equal to half the sum of the lengths of the two bases. • The properties of an isosceles trapezoid are: • The base angles are congruent. • The diagonals are congruent.
- 4. Kite • A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent. • The properties of a kite are: • The non-vertex angles are congruent. • The segment connecting the two vertex angles bisects the two vertex angles. • The diagonals are perpendicular. • The segment connecting the two vertex angles bisects the segment connecting the two non-vertex angles.