Find the sum of the measures of the interior angles of a convex 33-gon Find the sum of the measures of the interior angles of a convex 33-gon. If the measure of each interior angle of a regular polygon is 168°, find the number of sides in the polygon. Problem of the Day

Section 6-2 Parallelograms

Then Now Objectives You classified polygons with four sides as quadrilaterals. Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms.

Common Core State Standards Content Standards G.CO.11 – Prove theorems about parallelograms. G.GPE.4 – Use coordinates to prove simple geometric theorems algebraically. Mathematical Practices 3) Construct viable arguments and critique the reasoning of others. 4) Model with mathematics. Common Core State Standards

Parallelogram: a quadrilateral with both pairs of opposite sides parallel. Vocabulary

Properties of Parallelograms If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. If a parallelogram has one right angle, then it has four right angles Properties of Parallelograms

The wall-mounted mirror shown uses parallelograms that change shape as the arm is extended. In parallelogram JKLM, suppose m∠J = 47 and JK = 4. Find each measure. a) m∠L b) m∠M c) ML Example 1

To chart a course, sailors use a parallel ruler To chart a course, sailors use a parallel ruler. The rulers and the crossbars of the tool form parallelogram MNPQ. a) If m∠NMQ = 32, find m∠MNP b) If m∠MQP = 125, find m∠MNP. c) If MQ = 7 and MN = 3, find NP and PQ. Example 1

Diagonals of Parallelograms If a quadrilateral is a parallelogram, then its diagonals bisect each other. If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles. Diagonals of Parallelograms

Find the value of the variable in the given parallelogram. Example 2

Find the value of the variables in each parallelogram. Example 2

Determine the coordinates of the intersection of the diagonals of RSTU with vertices R(-8, -2), S(-6, 7), T(6, 7), and U(4, -2) Example 3

Determine the coordinates of the intersection of the diagonals of MNPR with vertices M(-3, 0), N(-1, 3), P(5, 4), and R(3, 1) Example 3

p.407 #9 – 21 odd, 31 – 36 all, 51, 53 Homework