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Mastering Triangles and Theorems: A Comprehensive Review

Explore relationships and theorems involving triangles, quadrilaterals, and polygons. Learn about different types of triangles such as acute, obtuse, and right triangles, along with properties like scalene, isosceles, and equilateral triangles.

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Mastering Triangles and Theorems: A Comprehensive Review

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  1. Review of Triangles SPI 3108.4.3      Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.

  2. Triangles • A triangle is a figure formed by three noncollinear points connected by three segments. All triangles can be classified by it’s side and by it’s angle. C a b A B c

  3. Acute Triangles • An acute triangle is a triangle with all acute angles. An acute triangle has three angles each less than 90 degrees. 80 50 50

  4. Obtuse Triangles • An obtuse triangle is a triangle with one obtuse angle (greater than 90 degrees) and two acute angles. 40 110 30

  5. A right triangle is a triangle with one right angle (equal to 90 degrees) and two acute angles. Right Triangles 45 90 45

  6. A scale triangle is a triangle with three unequal sides. Scalene Triangles 12 9 18

  7. An isosceles triangle is a triangle with (at least) two equal sides. Isosceles Triangles 14 14 12

  8. The Isosceles Triangle Theorem states if two sides of a triangle are congruent, then the angles opposite those sides are congruent. Isosceles Triangle Theorem 14 14 12

  9. Equilateral Triangles • An equilateral triangle is a triangle with all three sides of equal length. Since all three sides are equal; therefore, all three angles are equal also.

  10. Parts of Right Triangles • A right triangle has two legs and an hypotenuse. The hypotenuse is the side opposite of the right angle. The other two sides are called legs. Hypotenuse Leg Leg

  11. For a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The Pythagorean Theorem c a b

  12. Triangle Quiz • Please complete the following quiz that covers the information that was just presented to you.

  13. Question 1 • If a triangle has three unequal sides it is a ______ triangle. • A) Scalene • B) Obtuse • C) Isosceles • Answer: • A) Scalene

  14. Question 2 • A triangle with (at least) two equal sides is a ______ triangle. • A) Scalene • B) Isosceles • C) Congruent • Answer: • B) Isosceles

  15. Question 3 • A triangle with all three sides of equal length is a ______ triangle. • A) Equilateral • B) Right • C) Equiangular • Answer: • A) Equilateral

  16. Question 4 • A triangle with an angle of 90° is a ______ triangle. • A) Acute • B) Right • C) Congruent • Answer: • B) Right

  17. Question 5 • A triangle in which all three angles are less than 90° is a ______ triangle. • A) Right • B) Acute • C) Scalene • Answer: • B) Acute

  18. Question 6 • A triangle in which one of the angles is greater than 90° is a ______ triangle. • A) Obtuse • B) Isosceles • C) Acute • Answer: • A) Obtuse

  19. Question 7 • What is the Hypotenuse of a right triangle? • A) The smallest angle. • B) The side opposite the right angle. • C) The right angle. • Answer: • B) The side opposite the right angle.

  20. Question 8 • The Pythagorean Theorem states … • A) pr2 • B) (a+b)2/2=c • C) a2+b2=c2 • Answer: • C) a2+b2=c2

  21. Question 9 • Use the Pythagorean Theorem to solve the following: • a = 5 • b = 12 • c = ? • Answer: • c = 13

  22. Question 10 • Use the Pythagorean Theorem to solve the following: • a = ? • b = 16 • c = 20 • Answer: • a = 12

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