Geometry and Measurement: TriangleTutorial

Geometry and Measurement: TriangleTutorial

Before you begin you will want to have paper and pencil for notes and a straight edge

(ruler).Click enter to go on

triangle

A geometric figure having three sides and three angles.

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Classifications

B y th e irs id es

B y th e iran g les

Trian g lesare c lass ifiedin tw o ways


Classifications By Sides

Scalene-all sides are of different lengths (no congruent sides)

Isosceles-two sides are the same length (two sides congruent)

Equilateral-all sides the same length (all sides congruent)


Draw a scalene triangle.

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Here is an example of a scalene triangle.

No congruent sides

8cm 5cm

11cm


Draw an isosceles triangle.

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Here is an example of an isosceles triangle.

6in 6in

4in

Two congruent sides

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Draw an equilateral triangle.



Here is an example of an equilateral triangle.

14 ft 14 ft

14 ft

All sides congruent



Classification by angles.

Acute - a triangle having all angles acute (smaller than 90º)

Right - a triangle with one right angle (90º)

Obtuse - a triangle with one obtuse angle (greater than 90º and smaller than180º)



Draw an acute triangle.

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Here is an example of an acute triangle.

70

56 54

All angles are less than 90



º

º

º º

Draw a right triangle.



Here is an example of a right triangle.

The “box” in the corner means 90 .

One right angle makes it a right triangle.



º

Draw an obtuse triangle.



Here is an example of an obtuse triangle.

100

50 30



º

º º

Triangle Fact

The sum of the angles in a triangle must equal 180

Add the angles in these two triangles…what do you get?

100

50 30

70

56 54



º

ºº

º

º º

Triangle Fact

70

56 54

100

50 30

100 50+ 30 180

74 56+54180



º

º º

º

º º

Find The Missing Angle

You can find the measure of a missing angle in a triangle by taking 180º and subtracting thetwo given angles. 40º 45º

?

180-40140 140

-45 95º

OR 40+45 85

180- 85 95º



Find The Missing Angle

1. Two angles in a triangle are 35º and 65º. Find the third side.





Missing Angle Answers

1. 180 - 65 - 35 = 80º

2. 180 - 15 - 100 = 65º

3. 180 - 60 - 60 = 60º

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Perimeter

The perimeter of any geometric figure can be found by adding thelengths of the sides.

13m 14m

24m

13m 14m+24m 51m



Find the perimeter of each triangle below

1.

15ft 20ft

23ft

2. 13.2in 15.4in 10.7in



Perimeter Answers

1.

15ft 20ft

23ft

2. 13.2in 15.4in 10.7in

15ft + 20ft + 23ft = 68ft

13.2in + 15.4in + 10.7in = 39.3in



Area

Finding the area of a triangle can be a little tricky. You must know two

pieces of information. You must know the height of the triangle and you must know the length of the base.



Base and Height

height

base

height

baseThe height and base ALWAYS meet at a

right angle.



Area Formula

The formula for the area of a triangle is ½ base X height.

This is the same as base X height ÷ 2



Area Example

6km 12km 5km

20km

Base = 20kmHeight = 5km

Area = (½)(20)(5)

= (10)(5)= 50 km2

Remember, all area answers must have an exponent of 2 on the label.



Find the area of the triangle below.

28yd

13yd15yd 21yd



Area Answer

28yd

13yd15yd 21yd

Base = 28ydHeight = 13yd

Area = (½)(28)(13)

= (14)(13)

= 182 yd2



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Geometry and Measurement: TriangleTutorial