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Understanding Triangles: Types, Properties, and Theorems

Explore the fascinating world of triangles with this comprehensive PowerPoint presentation. Learn about different types of triangles including acute, obtuse, right, scalene, isosceles, equilateral, and equiangular. Discover key properties such as the Hypotenuse and the Pythagorean Theorem. Test your knowledge with a quiz that reinforces what you’ve learned. This engaging resource is perfect for students and educators seeking to deepen their understanding of geometric principles. Visit www.worldofteaching.com for more free educational materials!

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Understanding Triangles: Types, Properties, and Theorems

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  1. The World Of Triangles Powerpoint hosted on www.worldofteaching.com Please visit for 100’s more free powerpoints

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

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

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

  5. Right Triangles • A right triangle is triangle with an angle of 90°.

  6. Scalene Triangles • A triangle with three unequal sides.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  23. 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. Question 9

  24. The Pythagorean Theorem states … A) pr2 B) (a+b)2/2=c C) a2+b2=c2 Answer: C) a2+b2=c2 Question 10

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

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