Get a ruler, protractor, and two sheets of copy paper.

6.1 The Polygon Angle – Sum Theorems Theorem 6.1 – Polygon Angle-Sum Theorem The sum of the measures of the interior angles of an n-gon is (n – 2) * 180.

Finding a Polygon Angle Sum What is the sum of the interior angle measures of a heptagon? Sum = (n – 2) * 180 = (7 – 2) * 180 = 5 * 180 = 900° The sum of the interior angle measures of a heptagon is 900°.

Finding a Polygon Angle Sum What is the sum of the interior angle measurements of a decagon?

An equilateral polygon is a polygon with all sides congruent. An equiangular polygon is a polygon with all angles congruent. A regular polygon is a polygon that is both equilateral and equiangular. Regular Polygon Equilateral Polygon Equiangular Polygon

Corollary to the Polygon Angle-Sum Theorem The measure of each interior angle of a regular n-gon is

Using the Polygon Angle-Sum Theorem What is the measure of each interior angle in one hexagonal facet?

Using the Polygon-Angle Theorem What is the measure of angle Y in pentagon TODAY?

Using the Polygon-Angle Theorem

Exterior Angles You can draw exterior angles at any vertex of a polygon.

Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Finding an Exterior Angle Measure What is the measure of angle 1 in the regular octagon?

6.2 Properties of Parallelograms A parallelogram is a quadrilateral with both pairs of opposite sides parallel. In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

Finding an Exterior Angle Measure What is the measure of an exterior angle for a pentagon?

Theorem 6.3 If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Consecutive Angles Angles of a polygon that share a side are consecutive angles.

Theorem 6.4 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Theorem 6.5 If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Example 1 What are the measures of angles B, C, and D?

Theorem 6.6 If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Using Algebra to Find Lengths Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?

Using Algebra to Find Lengths