1. Sec 5.1 The World Of Triangles

2. Objectives---What we’ll learn… Identify triangles by angles (Acute, Right & Obtuse) Identify triangles by sides (Scalene, Isosceles & Equilateral)

3. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles equal 180°.

4. Acute Triangles A triangle in which all three angles are less than 90°.

5. Obtuse Triangles An obtuse triangle is a triangle in which one of the angles is greater than 90°.

6. Right Triangles A right triangle is a triangle with a 90° angle.

7. Triangle Classification by Angles Equilangular 3 congruent angles Acute 3 acute angles Obtuse 1 obtuse angle Right 1 right angle

8. Scalene Triangles A triangle with three unequal sides.

9. Isosceles Triangles An isosceles triangle is a triangle with (at least) two congruent sides and two congruent angles.

10. Isosceles Triangle Theorem The following shows that if two sides of a triangle are congruent, then the angles opposite those sides are congruent.

11. Equilateral Triangles An equilateral triangle is a triangle with all three sides of equal length.

12. Triangle Classification by Sides Equilateral 3 congruent sides 3 congruent angles Isosceles At least 2 congruent sides At least 2 congruent angles Scalene No congruent sides No congruent angles

13. Equiangular Triangles An equiangular triangle is a triangle which has three equal angles.

14. Congruent Triangles Congruent triangles are triangles whose corresponding angles and sides are congruent. They are exactly the same size and shape.

15. The Hypotenuse The hypotenuse of a right triangle is the triangle's longest side, i.e., the side opposite to the right angle.

16. The Pythagorean Theorem For a right triangle with legs a and b and hypotenuse c, a 2 +b 2 =c 2.

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

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

19. Question 2 A triangle which has three equal angles is a ______ triangle.  A) Acute  B) Equilateral  C) Equiangular Answer:  C) Equiangular

20. Question 3 A triangle with (at least) two equal sides is a ______ triangle.  A) Scalene  B) Isosceles  C) Congruent Answer:  B) Isosceles

21. Question 4 Two triangles that are equal are called ______ triangles  A) Acute  B) Obtuse  C) Congruent Answer:  C) Congruent

22. Question 5 A triangle with all three sides of equal length is a ______ triangle.  A) Equilateral  B) Right  C) Equiangular Answer:  A) Equilateral

23. Question 6 A triangle with an angle of 90° is a ______ triangle.  A) Acute  B) Right  C) Congruent Answer:  B) Right

24. Question 7 A triangle in which all three angles are less than 90° is a ______ triangle.  A) Right  B) Acute  C) Scalene Answer:  B) Acute

25. Question 8 A triangle in which one of the angles is greater than 90° is a ______ triangle.  A) Obtuse  B) Isosceles  C) Acute Answer:  A) Obtuse

26. Question 9 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.

27. Question 10 The Pythagorean Theorem states …  A)  r 2  B) (a+b) 2 /2=c  C) a 2 +b 2 =c 2 Answer:  C) a 2 +b 2 =c 2

28. Question 11 Use the Pythagorean Theorem to solve the following:  a = 5  b = 12  c = ? Answer:  c = 13

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