The World Of Triangles

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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, 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) πr2

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