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Applying Triangle Sum Properties

Applying Triangle Sum Properties. Section 4.1. Triangles. Triangles are polygons with three sides. There are several types of triangle: Scalene Isosceles Equilateral Equiangular Obtuse Acute Right. Scalene Triangles. Scalene triangles do not have any congruent sides.

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Applying Triangle Sum Properties

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  1. Applying Triangle Sum Properties Section 4.1

  2. Triangles • Triangles are polygons with three sides. • There are several types of triangle: • Scalene • Isosceles • Equilateral • Equiangular • Obtuse • Acute • Right

  3. Scalene Triangles • Scalene triangles do not have any congruent sides. • In other words, no side has the same length. 6cm 3cm 8cm

  4. Isosceles Triangle • A triangle with 2 congruent sides. • 2 sides of the triangle will have the same length. • 2 of the angles will also have the same angle measure.

  5. Equilateral Triangles • All sides have the same length

  6. Equiangular Triangles • All angles have the same angle measure.

  7. Obtuse Angle • Will have one obtuse angle.

  8. Acute Triangle • All angles are acute angles.

  9. Right Triangle • Will have one right angle.

  10. Exterior Angles vs. Interior Angles • Exterior Angles are angles that are on the outside of a figure. • Interior Angles are angles on the inside of a figure.

  11. Interior or Exterior?

  12. Interior or Exterior?

  13. Interior or Exterior?

  14. Triangle Sum Theorem (Postulate Sheet) • States that the sum of the interior angles is 180. • We will do algebraic problems using this theorem. The sum of the angles is 180, so x + 3x + 56= 180 4x + 56= 180 4x = 124 x = 31

  15. Find the Value for X 2x + 15 + 3x + 90 = 180 2x + 15 5x + 105 = 180 5x = 75 3x x = 15

  16. Corollary to the Triangle Sum Theorem (Postulate Sheet) • Acute angles of a right triangle are complementary. 3x + 10 3x + 10 5x +16 20

  17. Exterior Angle Sum Theorem • The measure of the exterior angle of a triangle is equal to the sum of the non-adjacent interior angles of the triangle

  18. 88 + 70 = y 158 = y

  19. 2x + 40 = x + 72 • 2x = x + 32 • x = 32

  20. Find x and y 46o 8x - 1 2yo 3x + 13

  21. Page 221 • #1 – 10, 14 – 30

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