warm up 1. find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. find the area of...

Warm Up

1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft.

3. Find the area of a parallelogram with height 9 in. and base length 15 in.

2. Find the area of a rectangle with side lengths 24 in. and 32 in.

64 ft

768 in2

135 in2

Pre-Algebra

2

Pre-Algebra

Exploring

Triangles

3

Naming Triangles

For example, we can call the following triangle:

Triangles are named by using its vertices.

∆ABC ∆BAC

∆CAB ∆CBA∆BCA

∆ACB

A

B

C

4

Opposite Sides and Angles

A

B C

Opposite Sides:

Side opposite to A :

Side opposite to B :

Side opposite to C :

Opposite Angles:

Angle opposite to : A

Angle opposite to : B

Angle opposite to : C

BC

AC

AB

BC

AC

AB

5

Classifying Triangles by Sides

Equilateral:

Scalene: A triangle in which all 3 sides are different lengths.

Isosceles: A triangle in which at least 2 sides are equal.

A triangle in which all 3 sides are equal.

AB

= 3

.02

cm

AC

= 3.15 cm

BC = 3.55 cm

A

B CAB =

3.47

cmAC = 3.47 cm

BC = 5.16 cmBC

A

HI = 3.70 cm

G

H I

GH = 3.70 cm

GI = 3.70 cm

6

Classifying Triangles by Angles

Acute:

Obtuse:

A triangle in which all 3 angles are less than 90˚.

A triangle in which one and only one angle is greater than 90˚& less than 180˚

108°

44°

28°B

C

A

57 ° 47°

76°

G

H I

7

Classifying Triangles by Angles

Right:

Equiangular:

A triangle in which one and only one angle is 90˚

A triangle in which all 3 angles are the same measure.

34

56

90B C

A

60

6060C

B

A

8

polygons

Classification by Sides with Flow Charts & Venn Diagrams

triangles

Scalene

Equilateral

Isosceles

Triangle

Polygon

scalene

isosceles

equilateral

9

polygons

Classification by Angles with Flow Charts & Venn Diagrams

triangles

Right

Equiangular

Acute

Triangle

Polygon

right

acute

equiangular

Obtuse

obtuse

10

Theorems & Corollaries

The sum of the interior angles in a triangle is 180˚.

Triangle Sum Theorem:

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.

Example 1: Finding the Perimeter of Triangles

A. 4

10= 21 units

7

P = 4 + 7 + 10

Add all sides.

Find the perimeter of each figure.

B.6

11

P = 9 + 6 + 119

= 26 units

A triangle can be thought of as half of a parallelogram.

Triangle: The area A of a triangle is one-half the base length b times the height h.

AREA OF A TRIANGLEWords Numbers Formula

A = (8)(4) = 16 units2

1 2

A. (–2, 2), (4, 2), (0, 5)

x

y

6

3

= 9 units2

A = bh12

Additional Example 2A: Finding the Area of Triangles Graph and find the area of the figure with the given vertices.

(4, 2)

(0, 5)

(–2, 2)= • 6 • 31

2

Area of a triangle

Substitute for b and h.

A. (–1, 1), (1, 7), (7, 1)

Try This: Example 2A

Graph and find the area of the figure with the given vertices.

x

y

8

(1, 7)

(–1, 1) (7, 1)= 24 units2

A = bh12

= • 8 • 612

Area of a triangle

Substitute for b and h.6

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:

Classify by angles:

alsoIsosceles Triangle

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: