Download Introduction to Quadrilaterals

January 17, 2017
Unit 7 Lesson 1
Introduction to
Quadrilaterals
It is easier to square the circle than to get round a
mathematician.
- Augustus De Morgan
Quadrilaterals have four vertices and sides such that:
1. Each segment intersects two other segments at their endpoints
2. No two segments with a common endpoint are collinear
Quadrilateral
Not a Quadrilateral
January 17, 2017
How to Name a Quadrilateral:
We use the points (vertices) in a clockwise
(or counter-clockwise) pattern to name.
Quadrilateral ABCD; CBAD; BCBA
What would ACBD look like? Is this a quadrilateral?
A convex quadrilateral is a quadrilateral such that no line
containing a side passes through the interior of the quadrilateral.
A non-convex quadrilateral is calledconcave.
Note: When talking about quadrilaterals it will
be a convex unless told otherwise.
Convex
Concave
January 17, 2017
What is the interior angle sum of a convex quadrilateral?
How can you show this?
What is the sum of the exterior angles of a convex quadrilateral?
How can we show this?
(Note: an exterior angle is formed by extending a side
of the quadrilateral just like we did with triangles)
January 17, 2017
What are some theorems (shortcuts) to show two
quadrilaterals are congruent?
Example 1: Quadrilateral MNOP has exteriors angles
in the ratio 3:4:5:6 (in this order).
What are the measures of the interior angles?
January 17, 2017
Example 2: Are the quadrilaterals congruent? If so, state why and
write a congruence statement.
Example 3:
In example 1, what was special
about the quadrilateral and why?
What type of special quadrilateral
would it have to be?
January 17, 2017