Geom 4point1

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Geom 4point1

  1. 1. 4.1 Triangles and Angles Objectives: - Classify triangles by their sides and angles - Find angle measures
  2. 2. Names of Triangles - by sides <ul><li>Equilateral </li></ul><ul><ul><li>3 congruent sides </li></ul></ul><ul><li>Isosceles </li></ul><ul><ul><li>At least 2 congruent sides </li></ul></ul><ul><li>Scalene </li></ul><ul><ul><li>No congruent sides </li></ul></ul>
  3. 3. Names of Triangles - by angles <ul><li>Acute </li></ul><ul><ul><li>3 acute angles </li></ul></ul><ul><li>Equilateral </li></ul><ul><ul><li>3 congruent angles </li></ul></ul><ul><li>Right </li></ul><ul><ul><li>1 right angle </li></ul></ul><ul><li>Obtuse </li></ul><ul><ul><li>1 obtuse angle </li></ul></ul>
  4. 4. When you classify a triangle... <ul><li>Be as specific as possible. </li></ul><ul><li>acute scalene </li></ul>A B C 65˚ 57˚ 58˚
  5. 5. When you classify a triangle... <ul><li>What is this one? </li></ul><ul><li>obtuse isosceles </li></ul>120˚
  6. 6. Terms <ul><li>Each of the 3 points joining the sides of a triangle is a vertex </li></ul><ul><li>2 sides sharing a common vertex are adjacent sides </li></ul>A B C
  7. 7. Right Triangles <ul><li>In a right triangle, the side opposite the right angle is called the hypotenuse </li></ul><ul><li>The sides opposite the two acute angles are called legs </li></ul>A B C 50° q r s
  8. 8. Isosceles Triangles <ul><li>If an isosceles triangle has 3 congruent sides, it is equilateral. </li></ul><ul><li>If an isosceles triangle has 2 congruent sides, the sides are the legs of the triangle, and the 3rd side is the base of the triangle. </li></ul>
  9. 9. Identifying parts <ul><li>What kind of triangle is this? </li></ul><ul><li>isosceles right </li></ul><ul><li>Which side is the hypotenuse? </li></ul><ul><li>Which side is the base? </li></ul><ul><li>Which sides are the legs? </li></ul>5” 5” 7”
  10. 10. Interior & Exterior Angles <ul><li>Interior angles are inside the triangle. </li></ul><ul><li>Exterior angles are adjacent to the interior angles. </li></ul><ul><li>Each vertex has a pair of congruent exterior angles. </li></ul>
  11. 11. Triangle Sum Theorem <ul><li>The sum of the measures of the interior angles of a triangle is 180˚. </li></ul>
  12. 12. Exterior Angle Theorem <ul><li>The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. </li></ul>
  13. 13. Corollary <ul><li>A corollary to a theorem is a statement that can be proved easily using the theorem. </li></ul>
  14. 14. Corollary to the Triangle Sum Theorem: <ul><li>The acute angles of a right triangle are complementary. </li></ul>
  15. 15. Classwork <ul><li>Do p. 198 1-15 together </li></ul>

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