Geometry CP, Feb 1
Chapter 6 Review
Book Section: 6-1 – 6-6
Essential Question: What do I need to know to pass this unit test?
Standards: CCSS G.CO.10, G.MG.3; G-3.5
Polygon Angles
• Polygon Angles (convex polygons) Theorems 6.1-6.2
 Interior angles sum formula is (n-2)180 for an n-sided
polygon(6.3)
 The sum of exterior angles of any convex polygon is 360 (6.2)
Properties of Parallelograms
• Parallelograms have a set of unique properties that are
defined by theorems 6.3-6.6, which are: In a
parallelogram
 Opposite sides are congruent (6.3)
 Opposite angles are congruent (6.4)
 Consecutive angles are supplementary (6.5)
 If a parallelogram has a right angle, it has 4 right angles (6.6)
Parallelograms and Diagonals
• Parallelogram’s diagonals also have properties that are
defined by theorems 6.7-6.8, which are: In a
parallelogram
 The diagonals bisect each other (6.7)
 Each diagonal separates the quadrilateral into two congruent
triangles (6.8)
Proving it is a Parallelogram
• You can prove that a quadrilateral is a parallelogram by
using theorems 6.9-6.12, which state that: You have a
parallelogram if:
 Both pairs of opposite sides are congruent (6.9)
 Both pairs of opposite angles are congruent (6.10)
 If the diagonals bisect each other (6.11)
 If one pair of opposite sides is both parallel and
congruent(6.12)
Property of Rectangles
• Rectangles have a set a unique properties that is defined
by theorem 6.13, which is: In a rectangle
 Diagonals are congruent (6.13)
• This property can be used to prove a rectangle status
 If a parallelogram has congruent diagonals, it is a rectangle
(6.14)
Properties of Rhombi
• Rhombi have a set of unique properties that are defined
by theorems 6.15-6.16, which are: In a rhombus
 Diagonals are perpendicular (6.15)
 Diagonals bisect each pair of opposite angles (6.16)
Conditions for Rhombi and Squares
• To prove a parallelogram is a rhombus (or square) we
have theorems 6.17-6.20, which are:
 If the diagonals of a parallelogram are perpendicular then it is a
rhombus (6.17)
 If one diagonal of a parallelogram bisects a pair of opposite
angles then it is a rhombus (6.18)
 If one pair of consecutive sides of a parallelogram are
congruent then it is a rhombus (6.19)
 If a quadrilateral is both a rectangle and a rhombus then it is a
square (6.20)
What Should I Know?
• In addition to understanding and being able to apply each
of these theorems, know and understand each and every
homework problem that we have done in this chapter,
and understand when and how the Pythagorean Theorem
applies in relation to any quadrilateral application.
Isosceles Trapezoid Theorems
• Isosceles Trapezoids have a set of unique properties and
conditions that are defined by theorems 6.21-6.23, which
are: In an isosceles trapezoid
 Each pair of base angles are congruent (6.21)
• If
 One pair of base angles are congruent is a trapezoid, then it is
isosceles (6.22)
 The diagonals of a trapezoid are congruent if and only if it is
isosceles (6.23)
Midsegment Theorem
Kite Theorems
Examples
Group Mini-Project
Draw any shaped convex quadrilateral on a blank page.
Measure each side and find and mark each midpoint.
Connect the adjacent midpoints to construct another
quadrilateral. What type of shape do you think it is.
Measure your new shape side lengths and find and mark
midpoints. Draw the new quadrilateral, and do the process
one more time. How are all the new shapes related.
Make a group conjecture about your experience here.
Classwork: Group Proj and Review Sheet
Homework: Study for Test