Download Triangle

Pre-Algebra
Warm Up
1. Find the perimeter of a rectangle with side
lengths 12 ft and 20 ft.
64 ft
2. Find the area of a rectangle with side lengths 24
in. and 32 in.
768 in2
3. Find the area of a parallelogram with height 9
in. and base length 15 in.
135 in2
Pre-Algebra
Exploring
Triangles
2
Naming Triangles
Triangles are named by using its vertices.
For example, we can call the following triangle:
∆ABC
∆ACB
∆BAC
∆BCA
∆CAB
∆CBA
B
C
A
3
Opposite Sides and Angles
Opposite Sides:
A
Side opposite to A : BC
Side opposite to B : AC
Side opposite to C : AB
B
C
Opposite Angles:
Angle opposite to BC : A
Angle opposite to AC : B
Angle opposite to AB : C
4
Classifying Triangles by Sides
Scalene: A triangle in which all 3 sides are different lengths.
A
A
B
C
BC = 3.55 cm
B
C
BC = 5.16 cm
Isosceles: A triangle in which at least 2 sides are equal.
G
Equilateral: A triangle in which all 3 sides are equal.
GH = 3.70 cm
H
HI = 3.70 cm
5
I
Classifying Triangles by Angles
Acute: A triangle in which all 3 angles are less than 90˚.
G
76
57
47
H
Obtuse:
I
A
A triangle in which one and only one
angle is greater than 90˚& less than 180˚
44
28 108 C
B
6
Classifying Triangles by Angles
Right: A triangle in which one and only one angle is 90˚
A
56
B
90
34
C
Equiangular: A triangle in which all 3 angles are the same measure.
B
60
A
60
60
C
7
Classification by Sides
with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
scalene
Scalene
Isosceles
isosceles
equilateral
Equilateral
8
Classification by Angles
with Flow Charts & Venn Diagrams
Polygon
polygons
triangles
Triangle
right
acute
Right
Obtuse
Acute
Equiangular
equiangular
obtuse
9
Theorems & Corollaries
Triangle Sum Theorem:
The sum of the interior angles in a
triangle is 180˚.
Third Angle Theorem:
If two angles of one triangle are congruent to two angles of a second
triangle, then the third angles of the triangles are congruent.
Corollary 1: Each angle in an equiangular triangle is 60˚.
Corollary 2: Acute angles in a right triangle are complementary.
Corollary 3: There can be at most one right or obtuse angle in a
triangle.
10
Example 1: Finding the Perimeter of Triangles
Find the perimeter of each figure.
A.
7
4
Add all sides.
P = 4 + 7 + 10
10
= 21 units
9
6
B.
P = 9 + 6 + 11
= 26 units
11
A triangle can be thought of as half of a parallelogram.
AREA OF A TRIANGLE
Words
Triangle: The
area A of a
triangle is onehalf the base
length b times
the height h.
Numbers
A=
1
(8)(4)
2
= 16 units2
Formula
Additional Example 2A: Finding the Area of Triangles
Graph and find the area of the figure with the given
vertices.
A. (–2, 2), (4, 2), (0, 5)
Area of a triangle
y
A = 1 bh
2
(0, 5)
(–2, 2)
3
6
Substitute for b and h.
= 1 •6•3
2
(4, 2)
x
= 9 units2
Try This: Example 2A
Graph and find the area of the figure with the given
vertices.
A. (–1, 1), (1, 7), (7, 1)
Area of a triangle
y
(1, 7)
A = 1 bh
2
6
(7, 1)
(–1, 1)
8
x
Substitute for b and h.
= 1 •8•6
2
= 24 units2
Classifying
Triangles
by sides and angles
Beat the
Computer Drill
Directions:
When the slide appears, say BOTH
NAMES for the type of triangle aloud
before the computer shows you the
answer. Classify each triangle by both its
SIDES and its ANGLES. You will have 6
seconds.
Classify by
sides:
Classify by
angles:
Classify by
sides:
also
Isosceles
Triangle
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles:
Classify by
sides:
Classify by
angles: