1. PRE-ALGEBRA Find ALL of the missing angle measures. 40° 120° 60° 40 ° 60° 180-(40+60) = 80° 80° 100° Warm-Up for Lesson 9-3

2. PRE-ALGEBRA s t c d 1 2 34 5 6 78 9 10 11 12 13 14 1516 s || t and c || d. Name all the angles that are congruent to  1. Give a reason for each answer.  3   1 corresponding angles  6   1 vertical angles  8   1 alternate exterior angles  9   1 corresponding angles  1   11 corresponding angles  14   1 alternate exterior angles  1   16 alternate exterior angles Warm-Up for Lesson 9-3

3. PRE-ALGEBRA How can you classify a triangle by the lengths of its sides? How can you classify a triangle by the measures of its angles? Classifying Polygons (9-3)

4. PRE-ALGEBRA Classifying Polygons (9-3) quadrilateral – a four-sided shape par allelogram – two pairs of parallel sides How can you classify a quadrilateral by its sides and angles? rhombus – four congruent (equal) sides rectangle – four right angles square – four right angles and four congruent sides trapezoid – one pair of parallel sides kite – two pairs of congruent sides that are adjacent (next to one another)

5. PRE-ALGEBRA Classifying Polygons (9-3) What is a regular polygon? regular polygon – a polygon (many-sided shape) in which all sides and angles are congruent (equal). Examples: To find the sum of the interior angles, we divide the polygon into triangles. For example, there are three triangles in a pentagon, and because the sum of each triangle is 180°, we get 540°, so the measure of the interior angles of a regular pentagon is 540° and each angle is 540° / 5, or 108°.. There are four triangles in a hexagon, 180° x 4 = 720°, so the measure of the interior angles of a regular pentagon is 720° and each angle is 720° / 6, or 120°.

6. PRE-ALGEBRA Classify the triangle by its sides and angles. The triangle has no congruent sides and one obtuse angle. The triangle is a scalene obtuse triangle. Classifying Polygons LESSON 9-3 Additional Examples

7. PRE-ALGEBRA Name the types of quadrilaterals that have at least one pair of parallel sides. All parallelograms and trapezoids have at least one pair of parallel sides. Parallelograms include rectangles, rhombuses, and squares. Classifying Polygons LESSON 9-3 Additional Examples

8. PRE-ALGEBRA A contractor is framing the wooden deck shown below in the shape of a regular dodecagon (12 sides). Write a formula to find the perimeter of the deck. Evaluate the formula for a side length of 3 ft. To write a formula, let x = the length of each side. The perimeter of the regular dodecagon is x + x + x + x + x + x + x + x + x + x + x + x. Therefore a formula for the perimeter is P = 12x. P = 12xWrite the formula. = 12(3) Substitute 3 for x. = 36Simplify. For a side length of 3 ft, the perimeter is 36 ft. Classifying Polygons LESSON 9-3 Additional Examples