The World Of Triangles

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

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

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

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

Scalene Triangles  A triangle with three unequal sides.

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

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

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

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

Congruent Triangles   Congruent triangles are triangles whose corresponding angles and sides are congruent.

They are exactly the same size and shape.

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

The Pythagorean Theorem  For a right triangle with legs

a

and

b

and hypotenuse

c

, a 2 +b 2 =c 2 .

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

Question 1  If a triangle has three unequal sides it is a ______ triangle.

   A) Scalene B) Obtuse C) Isosceles  Answer:  A) Scalene

Question 2  A triangle which has three equal angles is a ______ triangle.

   A) Acute B) Equilateral C) Equiangular  Answer:  C) Equiangular

Question 3  A triangle with (at least) two equal sides is a ______ triangle.

   A) Scalene B) Isosceles C) Congruent  Answer:  B) Isosceles

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

Question 5  A triangle with all three sides of equal length is a ______ triangle.

   A) Equilateral B) Right C) Equiangular  Answer:  A) Equilateral

Question 6  A triangle with an angle of 90 ° is a ______ triangle.

   A) Acute B) Right C) Congruent  Answer:  B) Right

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

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

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.

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

Question 11  Use the Pythagorean Theorem to solve the following:    a = 5 b = 12 c = ?

 Answer:  c = 13

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