Review of Triangles

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