SPI 3108.4.3      Identify, describe and/or apply the relationships and

theorems involving different types of triangles, quadrilaterals and other

polygons.

A triangle is a figure formed by three noncollinear points connected by three segments. All triangles can be classified by it’s side and by it’s angle.

C

A B

a

b

c

An acute triangle is a triangle with all acute angles. An acute triangle has three angles each less than 90 degrees.

80

50 50

An obtuse triangle is a triangle with one obtuse angle (greater than 90 degrees) and two acute angles.

11030

40

A right triangle is a triangle with one right angle (equal to 90 degrees) and two acute angles.

90

45

45

A scale triangle is a triangle with three unequal sides.

12 9

18

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

12

14 14

The Isosceles Triangle Theorem states if two sides of a triangle are congruent, then the angles opposite those sides are congruent.

12

14 14

An equilateral triangle is a triangle with all three sides of equal length. Since all three sides are equal; therefore, all three angles are equal also.

A right triangle has two legs and an hypotenuse. The hypotenuse is the side opposite of the right angle. The other two sides are called legs.

Leg

Leg

Hypotenuse

For a right triangle with legs a and b and hypotenuse c, a2

+ b2 = c2. ca

b

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

If a triangle has three unequal sides it is a ______ triangle. A) Scalene B) Obtuse C) Isosceles

Answer: A) Scalene

A triangle with (at least) two equal sides is a ______ triangle. A) Scalene B) Isosceles C) Congruent

Answer: B) Isosceles

A triangle with all three sides of equal length is a ______ triangle. A) Equilateral B) Right C) Equiangular

Answer: A) Equilateral

A triangle with an angle of 90° is a ______ triangle. A) Acute B) Right C) Congruent

Answer: B) Right

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

Answer: B) Acute

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

Answer: A) Obtuse

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.

The Pythagorean Theorem states … A) r2

B) (a+b)2/2=c C) a2+b2=c2

Answer: C) a2+b2=c2

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

Answer: c = 13

Use the Pythagorean Theorem to solve the following: a = ? b = 16 c = 20

Answer: a = 12