Chapter 6 Quadrilaterals Section 6 1 Polygons Polygon
- Slides: 68
Chapter 6 Quadrilaterals
Section 6. 1 Polygons
Polygon • A polygon is formed by three or more segments called sides – No two sides with a common endpoint are collinear. – Each side intersects exactly two other sides, one at each endpoint. – Each endpoint of a side is a vertex of the polygon. – Polygons are named by listing the vertices consecutively.
Identifying polygons • State whether the figure is a polygon. If not, explain why.
Polygons are classified by the number of sides they have NUMBER OF SIDES 3 TYPE OF NUMBER POLYGON OF SIDES TYPE OF POLYGON triangle 8 octagon 4 quadrilateral 9 nonagon 5 pentagon 10 decagon 6 hexagon 12 dodecagon 7 heptagon N-gon
Two Types of Polygons: 1. Convex: If a line was extended from the sides of a polygon, it will NOT go through the interior of the polygon. Example:
2. Concave: If a line was extended from the sides of a polygon, it WILL go through the interior of the polygon. Example:
Regular Polygon • A polygon is regular if it is equilateral and equiangular • A polygon is equilateral if all of its sides are congruent • A polygon is equiangular if all of its interior angles are congruent
Diagonal • A segment that joins two nonconsecutive vertices.
Interior Angles of a Quadrilateral Theorem • The sum of the measures of the interior angles of a quadrilateral is 360° 2 1 3 4
Section 6. 2 Properties of Parallelograms
Parallelogram • A quadrilateral with both pairs of opposite sides parallel
Theorem 6. 2 • Opposite sides of a parallelogram are congruent.
Theorem 6. 3 • Opposite angles of a parallelogram are congruent
Theorem 6. 4 • Consecutive angles of a parallelogram are supplementary. 2 1 3 4
Theorem 6. 5 • Diagonals of a parallelogram bisect each other.
Section 6. 3 Proving Quadrilaterals are Parallelograms
Theorem 6. 6 To prove a quadrilateral is a parallelogram: • Both pairs of opposite sides are congruent
Theorem 6. 7 To prove a quadrilateral is a parallelogram: • Both pairs of opposite angles are congruent.
Theorem 6. 8 To prove a quadrilateral is a parallelogram: • An angle is supplementary to both of its consecutive angles. 2 1 3 4
Theorem 6. 9 To prove a quadrilateral is a parallelogram: • Diagonals bisect each other.
Theorem 6. 10 To prove a quadrilateral is a parallelogram: • One pair of opposite sides are congruent and parallel. > >
Section 6. 4 Types of parallelograms
Rhombus • Parallelogram with four congruent sides.
Properties of a rhombus • Diagonals of a rhombus are perpendicular.
Properties of a rhombus • Each Diagonal of a rhombus bisects a pair of opposite angles.
Rectangle • Parallelogram with four right angles.
Properties of a rectangle • Diagonals of a rectangle are congruent.
Square • Parallelogram with four congruent sides and four congruent angles. • Both a rhombus and rectangle.
Properties of a square • Diagonals of a square perpendicular.
Properties of a square • Each diagonal of a square bisects a pair of opposite angles. 45° 45°
Properties of a square • Diagonals of a square congruent.
3 -Way Tie Rectangle Rhombus Square
Section 6. 5 Trapezoids and Kites
Trapezoid • Quadrilateral with exactly one pair of parallel sides. • Parallel sides are the bases. • Two pairs of base angles. • Nonparallel sides are the legs. Base > Leg > Base
Isosceles Trapezoid • Legs of a trapezoid are congruent.
Theorem 6. 14 • Base angles of an isosceles trapezoid are congruent. > A D > B C
Theorem 6. 15 • If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid. > A D > B C ABCD is an isosceles trapezoid
Theorem 6. 16 • Diagonals of an isosceles trapezoid are congruent. > A D > ABCD is isosceles if and only if B C
Examples on Board
Midsegment of a trapezoid • Segment that connects the midpoints of its legs. Midsegment
Midsegment Theorem for trapezoids • Midsegment is parallel to each base and its length is one half the sum of the lengths of the bases. C B M N A D MN= (AD+BC)
Examples on Board
Kite • Quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Theorem 6. 18 • Diagonals of a kite are perpendicular. B A C D
Theorem 6. 19 • In a kite, exactly one pair of opposite angles are congruent. B A C D
Examples on Board
Pythagorean Theorem c a b
Section 6. 6 Special Quadrilaterals
Properties of Quadrilaterals Property Both pairs of opposite sides are congruent Rectangle Rhombus X Diagonals are congruent X X X Diagonals are perpendicular Square Kite X X Diagonals bisect one another X X Consecutive angles are supplementary X X X X Both pairs of opposite angles are congruent Trapezoid X
Properties of Quadrilaterals • Quadrilateral ABCD has at least one pair of opposite sides congruent. What kinds of quadrilaterals meet this condition? PARALLELOGRAM RECTANGLE SQUARE RHOMBUS ISOSCELES TRAPEZOID
Section 6. 7 Areas of Triangles and Quadrilaterals
Area Congruence Postulate • If two polygons are congruent, then they have the same area.
Area Addition Postulate • The area of a region is the sum of the areas of its non-overlapping parts.
Area Formulas PARALLELOGRAM A=bh RECTANGLE A=lw SQUARE TRIANGLE
Area Formulas RHOMBUS KITE
Area Formulas TRAPEZOID h
- Area of quadrilateral kite
- Unit 7 polygons and quadrilaterals
- Measurement of regular polygon
- Is any four sided polygon a quadrilateral
- Topic 6 quadrilaterals and other polygons answers
- Polygons with parallel sides
- Topic 6 quadrilaterals and other polygons answers
- How to tell if shapes are similar
- Not polygon
- Section 10 topic 3 inscribed polygons in a circle
- Geometry section 11-4 areas of regular polygons answers
- Chapter 6 quadrilaterals
- 7-2 similar polygons
- Concept mapping chapter 10 meiosis 1 and meiosis 2
- Determine whether the quadrilateral is a parallelogram.
- Consecutive angles are supplementary
- A quadrilateral with 4 acute angles
- Names for rhombus
- Jeopardy quadrilaterals
- Properties of a kite
- Is a rhombus a square
- Quadrilateral with one pair of parallel sides
- Do all quadrilaterals have lines of symmetry
- Quadrilateral
- Quadrilaterals real life
- Quadrilateral venn diagram
- Features of quadrilaterals
- Are trapezoids polygons
- Do parallelograms have right angles
- 4 pics 1 word angle
- Inscribed quadrilateral worksheet
- Quadrilaterals and coordinate proof unit test a
- A square is sometimes a rectangle
- 9-1 developing formulas for triangles and quadrilaterals
- Developing formulas for triangles and quadrilaterals
- Describing quadrilaterals
- Classify quadrilaterals
- Lesson 16-4 proving a quadrilateral is a square
- How to sort quadrilaterals
- 5 quadrilaterals
- Classify polygons worksheet
- Kite properties
- Lesson 15-2 trapezoids
- Developing formulas for triangles and quadrilaterals
- Triangles and quadrilaterals
- 6 types of quadrilaterals
- Is a rhombus a parallelogram
- Quadrilateral test review
- Developing formulas for triangles and quadrilaterals
- A midsegment of a trapezoid quizizz
- Which is not a parallelogram
- 5 quadrilaterals
- Parallelograms and rhombuses
- Geometry name
- Regular quadrilaterals
- Inscribed angle conjecture
- Describing quadrilaterals
- Vertex example
- What do these have in common
- Objectives of quadrilaterals
- Objectives of quadrilaterals
- Quadrilateral plane figure
- Quadrilaterals jeopardy
- Sorting quadrilaterals
- 5-4 special quadrilaterals
- Quadrilaterals foldable
- Two pairs of parallel sides
- Properties of kites
- Def of rectangle