2. Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length 15 in. 2. Find the area of a rectangle with side lengths 24 in. and 32 in. 64 ft 768 in 2 135 in 2 Pre-Algebra

3. 2 Exploring Triangles

4. 3 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB ∆CBA ∆BCA ∆ACB A B C

5. 4 Opposite Sides and Angles Opposite Sides: Side opposite to  A : Side opposite to  B : Side opposite to  C : Opposite Angles: Angle opposite to :  A Angle opposite to :  B Angle opposite to :  C

6. 5 Classifying Triangles by Sides Equilateral: Scalene: A triangle in which all 3 sides are different lengths. Isosceles: A triangle in which at least 2 sides are equal. A triangle in which all 3 sides are equal. AB = 3.02 cm AC = 3.15 cm BC =3.55 cm A B C AB = 3.47 cm AC = 3.47 cm BC =5.16 cm B C A HI =3.70 cm G H I GH = 3.70 cm GI = 3.70 cm

7. 6 Classifying Triangles by Angles Acute: Obtuse: A triangle in which all 3 angles are less than 90˚. A triangle in which one and only one angle is greater than 90˚& less than 180˚ 108  44  28  B C A 57  47  76  G HI

8. 7 Classifying Triangles by Angles Right: Equiangular: A triangle in which one and only one angle is 90˚ A triangle in which all 3 angles are the same measure.

9. 8 polygons Classification by Sides with Flow Charts & Venn Diagrams triangles Scalene Equilateral Isosceles Triangle Polygon scalene isosceles equilateral

10. 9 polygons Classification by Angles with Flow Charts & Venn Diagrams triangles Right Equiangular Acute Triangle Polygon right acute equiangular Obtuse obtuse

11. 10 Theorems & Corollaries The sum of the interior angles in a triangle is 180˚. Triangle Sum Theorem: Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Corollary 1: Each angle in an equiangular triangle is 60˚. Corollary 2: Acute angles in a right triangle are complementary. Corollary 3: There can be at most one right or obtuse angle in a triangle.

12. Example 1: Finding the Perimeter of Triangles A. 4 10 = 21 units 7 P = 4 + 7 + 10 Add all sides. Find the perimeter of each figure. B. 6 11 P = 9 + 6 + 11 9 = 26 units

13. A triangle can be thought of as half of a parallelogram.

14. Triangle: The area A of a triangle is one- half the base length b times the height h. AREA OF A TRIANGLE WordsNumbersFormula A = (8)(4) = 16 units 2 1212

15. A. (–2, 2), (4, 2), (0, 5) x y 6 3 = 9 units 2 A = bh 1212 Additional Example 2A: Finding the Area of Triangles Graph and find the area of the figure with the given vertices. (4, 2) (0, 5) (–2, 2) = 6 3 1212 Area of a triangle Substitute for b and h.

16. A. (–1, 1), (1, 7), (7, 1) Try This: Example 2A Graph and find the area of the figure with the given vertices. x y 8 (1, 7) (–1, 1) (7, 1) = 24 units 2 A = bh 1212 = 8 6 1212 Area of a triangle Substitute for b and h. 6

17. Classifying Triangles by sides and angles Beat the Computer Drill

18. Directions: When the slide appears, say BOTH NAMES for the type of triangle aloud before the computer shows you the answer. Classify each triangle by both its SIDES and its ANGLES. You will have 6 seconds.

19. Classify by sides: Classify by angles:

20. Classify by sides: Classify by angles: also Isosceles Triangle

21. Classify by sides: Classify by angles:

22. Classify by sides: Classify by angles:

23. Classify by sides: Classify by angles:

24. Classify by sides: Classify by angles:

25. Classify by sides: Classify by angles:

26. Classify by sides: Classify by angles:

27. Classify by sides: Classify by angles:

28. Classify by sides: Classify by angles: