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Triangles

Triangles. A triangle is a polygon with three sides. Classifying Triangles. We name a triangle using its vertices. For example,. ∆ABC. ∆ACB. ∆BAC. ∆BCA. ∆CAB. ∆CBA. We say that is opposite . What is opposite ?. What is opposite of ?. Opposite Sides and Angles. Sides

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Triangles

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  1. Triangles

  2. A triangle is a polygon with three sides.

  3. Classifying Triangles We name a triangle using its vertices. For example, ∆ABC ∆ACB ∆BAC ∆BCA ∆CAB ∆CBA

  4. We say that is opposite . What is opposite ? What is opposite of ? Opposite Sides and Angles

  5. Sides Scalene Isosceles Equilateral Angles Acute Right Obtuse Equiangular Triangles can be classified by their

  6. Equilateral Triangle A triangle in which all 3 sides are equal

  7. Isosceles Triangle A triangle in which at least 2 sides are equal

  8. Scalene Triangle A triangle in which all 3 sides are different lengths

  9. Acute Triangle A triangle in which all 3 angles are less than 90˚

  10. Right Triangle A triangle in which exactly one angle is 90˚

  11. Obtuse Triangle A triangle in which exactly one angle is greater than 90˚and less than 180˚

  12. Equiangular Triangle A triangle in which all 3 angles are the same measure.

  13. Angles When the sides of a polygon are extended, other angles are formed. The inside/original angles are the interior angles. The adjacent/outside angles that form linear pairs with the interior angles are the exterior angles. Interior angles 1 <1, <2, <3 4 2 3 5 6 Exterior angles <4, <5, <6

  14. TRIANGLE INVESTIGATION

  15. Triangle Sum Theorem The sum of the interior angles in a triangle is 180˚. 40 60 80

  16. Example: Find the value of x. 2x 3x x

  17. EXTERIOR TRIANGLE INVESTIGATION

  18. Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Remote Interior Angles A Exterior Angle B C D

  19. Example: Find the value of x. 70 (2x+10) x

  20. Corollary Definition: A corollary to a theorem is a statement that can be proven easily using another theorem.

  21. Third Angle Corollary If two angles in one triangle are congruent to two angles in another triangle, then the third angles are congruent.

  22. Equiangular Corollary Each angle in an equiangular triangle is 60˚.

  23. Right Angle Corollary There can be at most one right or obtuse angle in a triangle.

  24. Acute Corollary Acute angles in a right triangle are complementary.

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