The World Of Triangles

Triangles

• A triangle is a 3-sided polygon. Every triangle has three sides and three angles, which when added together 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, a2+b2=c2.

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) r2

– B) (a+b)2/2=c– C) a2+b2=c2

• Answer:– C) a2+b2=c2

Question 11

• Use the Pythagorean Theorem to solve the following:– a = 5– b = 12– c = ?

• Answer:– c = 13