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PRE-QUIZ #2: TRIANGLES

PRE-QUIZ #2: TRIANGLES. A three-sided polygon A triangle with no congruent sides A triangle with at least two congruent sides A triangle with all angles congruent The sum of the measures of the angles in a triangle. Parallel Lines and Triangles.

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PRE-QUIZ #2: TRIANGLES

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  1. PRE-QUIZ #2: TRIANGLES • A three-sided polygon • A triangle with no congruent sides • A triangle with at least two congruent sides • A triangle with all angles congruent • The sum of the measures of the angles in a triangle

  2. Parallel Lines and Triangles

  3. Optical art is a form of abstract art that creates special effects by using geometric patterns.

  4. If A, B, and C are any three noncollinear points, then the union of the segments AB, BC, and AC is called a triangle, and is denoted by ABC. B C A AB, BC, AC Definition: TRIANGLE three angles vertices A B C sides

  5. Classification of Triangles  According to its sides scalene triangle no sides congruent

  6. Classification of Triangles  According to its sides isosceles triangle at least two sides congruent

  7. Classification of Triangles  According to its sides equilateral triangle all sides congruent

  8. Classification of Triangles  According to its angles acute triangle 3 acute angles

  9. Classification of Triangles  According to its angles right triangle 1 right angle

  10. Classification of Triangles  According to its angles obtuse triangle 1 obtuse angle

  11. Classification of Triangles  According to its angles equiangular triangle 3 congruent angles

  12. Sum of the Measures of the Angles of a Triangle 4 5 3 2 1 m4 + m3 + m5 = 180 m1 + m3 + m2 = 180

  13. 3 2 1 Theorem: The sum of the measures of the angles of a triangle is 180. m1 + m2 + m3 = 180

  14. A G E 36 36 C B F Corollary: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. If B  G and C  E, then A  F.

  15. Corollary: Each angle of an equiangular triangle measures ____. 60

  16. Corollary: In a triangle, there can be at most one right angle, or at most one obtuse angle.

  17. Corollary: The acute angles of a right triangle are complementary. x (90 – x)

  18. 3 4 2 9 10 8 5 1 6 7 EXTERIOR ANGLE OF A TRIANGLE an angle that forms a linear pair with an angle of a triangle

  19. 3 4 2 9 10 8 1 5 6 7 REMOTE INTERIOR ANGLES the two non-adjacent interior angles of a triangle with respect to its exterior angle

  20. 2 5 3 1 4 Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. m5 = m2 + m3

  21. Possible or Impossible a. scalene right triangle b. isosceles obtuse triangle c. isosceles acute triangle d. equilateral right triangle e. isosceles equiangular triangle f. scalene acute triangle g. scalene equiangular triangle

  22. 41 57 1 Find the measure of the numbered angle.

  23. 3 43 126 2 1 Find the measures of the numbered angles.

  24. 93 2 12 1 3 25 Find the measures of the numbered angles.

  25. Find the measures of the numbered angles. 99 2 1 3

  26. 58 29 2 1 136 Find the measures of the numbered angles.

  27. Find the measures of the numbered angles. 2 106 3 5 4 52 1

  28. One of the acute angles of a right triangle has a measure that is five less than four times the measure of the other. Find the measures of the acute angles.

  29. The measure of an exterior angle of a triangle is 133. The measure of one of its remote interior angles is forty four less than twice the measure of the other. What are the measures of the remote interior angles?

  30. DRILL BOARD

  31. Always, Sometimes, Never • A triangle has three acute angles. • Equilateral triangles are isosceles. • An isosceles triangle is obtuse. • The measure of an exterior angle is greater than the sum of the measures of its remote interior angles.

  32. Always, Sometimes, Never • 5. In an obtuse triangle, the acute angles are complementary. • The sum of the measures of the angles of an acute triangle is 180. • An acute triangle is an equiangular triangle.

  33. Always, Sometimes, Never 8. An isosceles right triangle has two acute angles. 9. If the measure of each angle of a triangle is 60, then the triangle is isosceles. 10. If one of the exterior angles of a triangle is obtuse, then its remote interior angles are both acute.

  34. HOMEWORK # 19 Textbook pages 98-100: Numbers 1-4; 7-10; 13-29; 35-40 (to be checked on Monday)

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