QuadrilateralsLesson 6-1
Warm-up
Warm-upSolve the following triangles using the
Pythagorean Theorem a2 + b2 = c2
95
12 9
8
8√3
Warm-upFind the missing point given the following
information.
1. Point 1 (3, 8), Point 2 (5, 12), Midpoint (x, y)
2. Point 1 (-2, 5), Point 2 (3, -3), Midpoint (x, y)
3. Point 1 (2, 4), Point 2 (x, y), Midpoint (5, -1)
4. Point 1 (-1, 2), Point 2 (2, y), distance = 5
ParallelogramsA parallelogram is a quadrilateral with both
pairs of opposite sides parallel
Properties of ParallelogramsIts opposite sides are congruentIts opposite angles are congruentIts consecutive angles are supplementary
(add to 180°)Its diagonals bisect each other. (Cut each
other into 2 equal sections)
Let’s PracticeFind the value of each variable in the
parallelogram.
Let’s PracticeFind the value of each variable in the
parallelogram.
Types of ParallelogramsRhombus – a parallelogram with four congruent
sides.Rectangle – a parallelogram with four right angles.Square – a parallelogram four congruent sides and
four right angles.Rhombus Corollary – a quadrilateral is a rhombus
if and only if it has four congruent sides.Rectangle Corollary – a quadrilateral is a
rectangle if and only if it has four right angles.Square Corollary – a quadrilateral is a square if
and only if it is a rhombus and a rectangle.
Special Parallelogram PropertiesIf a parallelogram is a rhombus, its diagonals
are perpendicular.
If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles.
If a parallelogram is a rectangle, its diagonals are congruent.
Let’s PracticeClassify the special quadrilateral. Explain
your reasoning. Then find the values of x and y.
Let’s PracticeClassify the special quadrilateral. Explain
your reasoning. Then find the values of x and y.
Other QuadrilateralsTrapezoid – a quadrilateral with exactly one
pair of parallel sides.
Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Trapezoid VocabularyBase - the parallel sides are the bases.Base Angles - in a trapezoid, the two angles
that have that base as a side.Legs – the non-parallel sides of a trapezoid.Isosceles Trapezoid – a trapezoid where
both legs are congruent.Midsegment of a Trapezoid – the segment
that connects the midpoints of the legs of a trapezoid.
Trapezoid Properties For an isosceles trapezoid, each pair of base
angles is congruent.For an isosceles trapezoid, the diagonals are
congruent.Midsegment Theorem for Trapezoids –
the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
Kite PropertiesIts diagonals are perpendicularExactly one pair of opposite angles are
congruent.The diagonal between the non-congruent
angles bisects the diagonal between the congruent angles.
Let’s PracticeFind “x”.
Let’s Practice
Let’s Practice