Chapter 6.1
Common Core G.DRT.5 – Use Congruence…criteria
to solve problems and prove relationships in
geometric figures.
Objectives – To find the sum of the measures of
the interior and exterior angles of a polygon
Chapter 6.1 Notes
Polygon – is a simple, closed figure made with
straight lines.
vertex
side
vertex
side
Convex – has no indentation
Concave – has an indentation
Number of Sides
Type of Polygon
3
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Unadecagon
Dodecagon
n - gon
4
5
6
7
8
9
10
11
12
n
Equilateral –
Equiangular –
Regular –
Diagonal –
Interior Angles of a Quadrilateral – sum of the
interior angles of any Quad. is _ _ _ .
Polygon Angle-Sum Theorem
(n – 2) * 180 where n = the number of sides
Corrollary to the Polygon Angle-Sum Theorem
The measure of the interior angles of a regular
polygon is
𝑛 −2 ∗180
𝑛
Polygon Exterior Angle-Sum Theorem
360°
To find one exterior angle of a regular polgon
take
360 / n
Chapter 6.2
Common Core G.CO.11 & G.SRT.5 - Prove
theorems about parallelograms.
Objectives – To use relationships among sides,
angles, & diagonals of parallelograms
Chapter 6.2 Notes
Thm – Opposite sides are ≌
in a parallelogram
Thm – Opposite ∠’s are ≌
in a parallelogram
Thm – Consecutive ∠’s are
supp. in a parallelogram
Thm – Diagonals bisect each other
in a parallelogram
If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off
congruent segments on every transversal, then
they cut off congruent segments on every
transversal.
A
C
𝐴
𝐵
B
D
=
𝐶
𝐷
Chapter 6.3
Common Core G.CO.11 & G.SRT.5 - Prove
theorems about parallelograms….the diagonals
of a parallelogram bisect each other and its
converses…
Objectives – To determine whether a
quadrilateral is a parallelogram.
Chapter 6.3 Notes
The five ways of proving a quadrilateral is a parallelogram. (p.371)
1)
2)
3)
4)
5)
Chapter 6.4
Common Core G.CO.11 & G.SRT.5 – Prove
theorems about parallelograms…rectangles are
parallelograms with congruent diagonals.
Objectives – To define and classify special types
of parallelograms. To use properties of
diagonals of rhombuses and rectangles.
Chapter 6.4
Parallelogram – Quad. with 2 sets of
parallel sides
Rhombus – is a parallelogram with 4 ≌ sides
Rectangle – is a parallelogram with 4 rt. angles
Square - is a parallelogram with 4 ≌ sides
and four right angles
Thm – a parallelogram is a rhombus if and only if
its diagonal are perpendicular
Thm – a parallelogram is a rhombus if and only if
each diagonal bisects a pair of opposite angles
Thm - a parallelogram is a rectangle if and only if
its diagonals are congruent
Chapter 6.5
Common Core G.CO.11 & G.SRT.5 – Prove
theorems about parallelograms…rectangles are
parallelograms with congruent diagonals.
Objective – To determine whether a
parallelogram is a rhombus or rectangle.
Chapter 6.5
Parallelogram – Quad. with 2 sets of
parallel sides
Rhombus – is a parallelogram with 4 ≌ sides
Rectangle – is a parallelogram with 4 rt. Angles
Square - is a parallelogram with 4 ≌ sides
and four right angles
Ways to prove a Quad. is a Rhombus
1) Prove it is a parallelogram with 4 ≌ sides
2) Prove the quad. is a parallelogram and then
show diagonals are perpendicular
3) Prove the quad. is a parallelogram and then
show that the diagonals bisect the opposite
angles
Way to Prove a parallelogram is a
Rectangle
If the diagonals of a parallelogram are
congruent, then the parallelogram is a rectangle.
Property
Both pairs of opp.
sides are II
Exactly 1 pair of
opp. sides are II
All ∠’s are ≌
Diagonals are ⊥
Diagonals are ≌
Diagonals bisect
each other
Both pairs of opp.
Sides are ≌
Exactly 1 pair of
opp. sides are ≌
All sides are ≌
Rectangle
Rhombus
Square
Chapter 6.6
Common Core G.SRT.5 – Use
congruence…criteria to solve problems and
prove relationships in geometric figures.
Objective – To verify and use properties of
trapezoids and kites
Chapter 6.6 Notes
Quadrilateral
Kite
Parallelogram
Rhombus Rectangle
Square
Trapezoid
Isos. Trap.
Trapezoid – is a quadrilateral with exactly one
pair of parallel sides.
Isosceles Trapezoid – is a trapezoid with
congruent legs
Thm – If a trapezoid is isosceles, then each pair
of base angles is congruent
Thm – If a trapezoid has a pair of congruent base
angles, then it is an isosceles trapezoid.
Thm – a trapezoid is isosceles if and only if its
diagonals are congruent
Midsegment Thm 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
Thm – If a quadrilateral is a kite, then its
diagonals are perpendicular.
Thm - If a quadrilateral is a kite, then exactly one
pair of opposite angles are congruent
Property
Both pairs of opp.
sides are II
Exactly 1 pair of
opp. sides are II
All ∠’s are ≌
Diagonals are ⊥
Diagonals are ≌
Diagonals bisect
each other
Both pairs of opp.
Sides are ≌
Exactly 1 pair of
opp. sides are ≌
All sides are ≌
Rectangle
Rhombus
Square
Kite
Trapezoid