1. What will we accomplish? We will review the naming of polygons. We will discuss two ways to classify triangles We will classify quadrilaterals by their characteristics.

2. A polygon is a closed plane figure formed by three or more line segments. A regular polygon’s sides are all equal in length. Polygons are named by the number of their sides and angles.

3. Name of PolygonNumber of Sides 3 4 5 6 7 8 9 10 12 nn-gon Are you familiar with these terms? Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodegacon

4. Triangles are classified by their sides. They are also classified by their angles. Triangles and their Classification

5. Classify by sides…. Scalene triangles Isosceles triangles Equilateral triangles ?

6. Marks on the sides of a triangle show which sides have the same measure. No sides are congruent. Two sides are congruent. All sides are congruent.

7. Classifying Triangles by Lengths of Sides Classify the triangle. The sum of the lengths of the sides is 18 in. c = 6 6 in. N L c M c + (6 + 6) = 18 c + 12 = 18 – 12 =–12 6 in. Side c is 6 inches long. Because LMN has three congruent sides, it is equilateral.

8. Finding a missing side & classify. Triangle ABC has a perimeter of 24 cm. If two sides are 8cm and 6cm, what must the third side length be? Classify the triangle. s = 10 cm 6 cm. C A B s + (8 + 6) = 24 s + 14 = 24 – 14 =–14 8 cm This triangle is scalene. No sides are congruent.

9. The perimeter of this triangle is 30 cm. If side RP is 8 cm, what are the lengths of sides RM and PM? M P R s = 11 cm 2s + 8 = 30 2s = 22 – 8 =– 8 ___ ___ 2 2

10. 10mm 2mm isosceles 5 cm 4 cm 6 cm scalene 4 in 7 in isosceles

11. The lengths of three sides of a triangle are given. Classify the triangle. ***** 1. 12, 12, 12 2. 28, 15, 14 3. 19, 19, 36 4. 25, 36, 12 equilateral scalene isosceles scalene

12. Classify by angles…. Right triangles Acute triangles Obtuse triangles ?

13. The sum of the measures of the angles in any triangle is 180°. You can see this if you tear the corners from a triangle and arrange them around a point on a line. Acute angles? Right angles? Obtuse angles? Straight angles? 90 degrees less than 90 degrees more than 90 degrees, less than 180 180

14. A right triangle has one right angle. Remember……..A triangle is a closed figure with three line segments and three angles. Triangles can be classified by the measures of their angles. An acute triangle has only acute angles An obtuse triangle has one obtuse angle. Acute triangle Right triangle Obtuse triangle

15. Lesson Quiz If the angles can form a triangle, classify the triangle as acute, obtuse, or right. 1. 37°, 53°, 90° 2. 65°, 110°, 25° 3. 61°, 78°, 41°4. 115°, 25°, 40° not a triangle right acute obtuse

16. Lesson Quiz If the angles can form a triangle, classify the triangle as acute, obtuse, or right. 1. 37°, 53°, 90° 2. 65°, 110°, 25° 3. 61°, 78°, 41°4. 115°, 25°, 40°

17. Ratios and Triangle Measures You can use a ratio box and proportions to find the measures of a triangle. Remember……the three measures total 180. ° If we know that the ratio of the angles in a triangle are in the ratio of 4:11:30, we can find the measures!! Ratio Angle measure 4 11 30 Let’s find the ratio total. 45 We know the sum of the angles…. 180 Use proportional reasoning to find the measures of the angles….. 120 16 11(4) ?? 44

18. The Wonderful World of Quadrilaterals

19. We will learn to identify, classify, and compare quadrilaterals. parallelogram trapezoid rectangle square rhombus kite

20. Parallelogram Parallelogram with four right angles. Trapezoid Rhombus Parallelogram with four congruent sides. Rectangle Square Rectangle with four congruent sides. Opposite sides are parallel and congruent. Opposite angles are congruent. Quadrilateral with exactly two parallel sides. May have two right angles. Kite Quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

21. QuadrilateralParallelogramRhombusRectangleSquareTrapezoidKite A quadrilateral is a plane figure with four sides and four angles. A parallelogram is a quadrilateral with opposite sides equal and parallel. A rhombus is a parallelogram with four equal sides A rectangle is a parallelogram with opposite sides equal and Parallel and four right angles A square is a rectangle with four equal sides. A trapezoid is a quadrilateral with ONLY one pair of parallel sides. A quadrilateral with two sets of adjacent, congruent sides.

22. QuadrilateralParallelogramRhombusRectangleSquareTrapezoidKite A quadrilateral is a plane figure with four sides and four angles. A parallelogram is a quadrilateral with opposite sides equal and parallel. A rhombus is a parallelogram with four equal sides A rectangle is a parallelogram with opposite sides equal and Parallel and four right angles A square is a rectangle with four equal sides. A trapezoid is a quadrilateral with ONLY one pair of parallel sides. A quadrilateral with two sets of adjacent, congruent sides.

23. Review Discussion Complete each statement. 1. A quadrilateral with four right angles is a _________. 2. A parallelogram with four right angles and four congruent sides is a _______. 3. A figure with 4 sides and 4 angles is a ______. 4. Give the most descriptive name for this quadrilateral. square square or rectangle quadrilateral trapezoid ? ? ?

24. True or false? 5. A rectangle is always a square but a square is not always a rectangle. 6. A square is always a rhombus but rhombus is not always a square. 7. All rectangles are regular polygons. 8. Squares and rhombi are regular quadrilaterals. true false true

25. What have we accomplished? We have named and classified polygons.