Download The World Of Triangles

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
c
B

An acute triangle
is a triangle with
all acute angles.
An acute triangle
has three angles
each less than 90
50
degrees.
80
50

An obtuse triangle
is a triangle with
one obtuse angle
(greater than 90
degrees) and two
acute angles.
40
30
110
45

A right triangle
is a triangle with
one right angle
(equal to 90
degrees) and two
acute angles.
90
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.
14
14
12

The Isosceles
Triangle Theorem
states if two sides
of a triangle are
congruent, then the
angles opposite
those sides are
congruent.
14
14
12

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.
Hypotenuse
Leg
Leg

For a right triangle
with legs a and b
and hypotenuse c,
a2 + b2 = c2.
c
a
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) pr2
 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