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Warm Up

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

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Warm Up

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  1. Pre-Algebra Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 64 ft 2. Find the area of a rectangle with side lengths 24 in. and 32 in. 768 in2 3. Find the area of a parallelogram with height 9 in. and base length 15 in. 135 in2

  2. Exploring Triangles Pre-Algebra

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

  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

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

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

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

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

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

  10. Theorems & Corollaries Triangle Sum Theorem: The sum of the interior angles in a triangle is 180˚. 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. There can be at most one right or obtuse angle in a triangle. Corollary 3:

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

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

  13. A = (8)(4) = 16 units2 1 2 Triangle: The area A of a triangle is one-half the base length b times the height h.

  14. y 1 2 A =bh 1 2 = • 6 • 3 x Additional Example 2A: Finding the Area of Triangles Graph and find the area of the figure with the given vertices. A. (–2, 2), (4, 2), (0, 5) Area of a triangle (0, 5) Substitute for b and h. 3 (–2, 2) (4, 2) 6 = 9 units2

  15. y 1 2 A =bh 1 2 = • 8 • 6 x Try This: Example 2A Graph and find the area of the figure with the given vertices. A. (–1, 1), (1, 7), (7, 1) Area of a triangle (1, 7) Substitute for b and h. 6 (7, 1) (–1, 1) = 24 units2 8

  16. Classifying Trianglesby sides and angles Beat the Computer Drill

  17. 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.

  18. Classify by sides: Classify by angles:

  19. Classify by sides: Classify by angles: Equilateral Triangle Acute Triangle also Isosceles Triangle

  20. Classify by sides: Classify by angles:

  21. Classify by sides: Classify by angles: Isosceles Triangle Obtuse Triangle

  22. Classify by sides: Classify by angles:

  23. Classify by sides: Classify by angles: Isosceles Triangle Acute Triangle

  24. Classify by sides: Classify by angles:

  25. Classify by sides: Classify by angles: Scalene Triangle Obtuse Triangle

  26. Classify by sides: Classify by angles:

  27. Classify by sides: Classify by angles: Scalene Triangle Right Triangle

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