homework Classifying Quadrilaterals Only ODD

Lesson 6.15 Quadrilaterals

Objectives To identify any quadrilateral, by name, as specifically as you can, based on its characteristics

Quadrilateral a quadrilateral is a polygon with 4 sides.

Specific Quadrilaterals There are several specific types of quadrilaterals. They are classified based on their sides or angles.

A quadrilateral simply has 4 sides – no other special requirements.

Examples of Quadrilaterals

A parallelogram has two pairs of parallel sides.

Parallelogram Two pairs of parallel sides opposite sides are actually congruent.

Parallelogram In a parallelogram opposite sides are equaland parallel. The diagonals of a parallelogram bisect each other. A parallelogram has rotational symmetry of order 2.

A rhombus is a parallelogram that has four congruent sides.

Rhombus Still has two pairs of parallel sides; with opposite sides congruent. 4 in.

Rhombus A rhombus is a parallelogramwith four equal sides. The diagonals of a rhombus bisect each other at right angles. A rhombus has two lines of symmetry and it has rotational symmetry of order 2.

A rectangle has four right angles.

Rectangle Still has two pairs of parallel sides; with opposite sides congruent. Has four right angles

Rectangle A rectangle has opposite sides of equal length A rectangle has two lines of symmetry. and four right angles.

A square is a specific case of both a rhombus AND a rectangle, having four right angles and 4 congruent sides.

Square Still has two pairs of parallel sides. Has four congruent sides Has four right angles

Square A square has four equal sidesand four right angles. It has four lines of symmetry and rotational symmetry of order 4.

A trapezoid has only one pair of parallel sides.

An isosceles trapezoid is a trapeziod with the non-parallel sides congruent.

Trapezoid has one pair of parallel sides. Isosceles trapezoid trapezoids (Each of these examples shown has top and bottom sides parallel.)

Trapezium A trapezium has one pair of opposite sides that are parallel. Can a trapezium have any lines of symmetry? Can a trapezium have rotational symmetry?

Isosceles trapezium In an isosceles trapezium the two opposite non-parallel sides are the same length. The diagonals of an isosceles trapezium are the same length. It has one line of symmetry.

An kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent congruent sides.

Example of a Kite 2 in. 4 in. 2 in.

Kite A kite has two pairs of adjacent sides of equal length. The diagonals of a kite cross at right angles. A kite has one line of symmetry.

Special Quadrilaterals A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and right angles. A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. A trapezoid is a quadrilateral with exactly one pair of parallel sides. The isosceles trapezoid at the right is a trapezoid whose nonparallel sides (legs) are congruent.

Quadrilateral Parallelogram Trapezoid Rhombus Rectangle Square

What are all of the names for this polygon?  Quadrilateral  Parallelogram  Rectangle Which name best describes the shape?

What are all of the names for this polygon?  Quadrilateral  Parallelogram Which name best describes the shape?

What are all of the names for this polygon?  Quadrilateral  Parallelogram  Rhombus Which name best describes the shape?

What are all of the names for this polygon?  Quadrilateral  Trapezoid Which name best describes the shape?

What are all of the names for this polygon?  Quadrilateral  Parallelogram  Square  Rhombus  Rectangle Which name best describes the shape?

Using Properties Find the value of the variables for the kite: x + 6 3x - 5 2x + 4 2y + 5 T K B J JB = KB 2x + 4 = 3x – 5 -x = -9 x = 9 TK = TK = 15 TJ => 2y + 5 = 15 2y = 10 y = 5

Using Properties Find the values of the variables for the rhombus: 3b + 2 3a + 8 4b - 2 5a + 4 3b + 2 = 4b -2 b = 4 5a + 4 = 3a + 8 2a = 4 a = 2

Complete each statement. 1. A quadrilateral with four right angles is a _________. 2. A parallelogram with four right angles and four congruent sides is a _______. 3. A figure with 4 sides and 4 angles is a ______. 4. Give the most descriptive name for this quadrilateral. Lesson Quiz square square or rectangle quadrilateral trapezoid

Interior Angles Interior angles: An interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint Interior angles of a quadrilateral always equal 360 degrees