Triangles:

             

A triangle has three sides and three angles

               

The three angles always add to 180°

           

Equilateral, Isosceles and Scalene       

           

There are three special names given to triangles that tell how many sides (or angles) are equal.

           

            There can be 3, 2 or no equal sides/angles:

           

                            Equilateral Triangle

               

Three equal sides

Three equal angles, always 60°

                Isosceles Triangle

 

Two equal sides

        Two equal angles               

                Scalene Triangle

               

No equal sides

No equal angles

           

           

           

What Type of Angle?

           

           

Triangles can also have names that tell you what type of angle is inside:

           

           

                        Acute Triangle

               

All angles are less than 90°               

                        Right Triangle

               

Has a right angle (90°)               

                        Obtuse Triangle               

Has an angle more than 90°                 

           

Combining the Names

            Sometimes a triangle will have two names, for example:

           

           

Right Isosceles Triangle

                   

Has a right angle (90°), and also two equal angles

                   

Can you guess what the equal angles are?               

           

Play With It ...

           

Try dragging the points around and make different triangles:

               

You might also like to play with the Interactive Triangle.

                       

Perimeter

The perimeter is the distance around the edge of the triangle: just add up the three sides:

Area

The area is half of the base times height.

  • "b" is the distance along the base
  • "h" is the height (measured at right angles to the base)

Area = ½ × b × h

       

The formula works for all triangles.

           

Note: a simpler way of writing the formula is bh/2

           

           

Example: What is the area of this triangle?

           

           

(Note: 12 is the height, not the length of the left-hand side)

           

           

Height = h = 12

                   

Base = b = 20

                   

Area = ½ × b × h = ½ × 20 × 12 = 120               

           

       

The base can be any side, Just be sure the "height" is measured at right angles to the "base":

(Note: You can also calculate the area from the lengths of all three sides using Heron's Formula.)

   

       

Why is the Area "Half of bh"?

       

Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (a parallelogram) which can be changed to a simple rectangle:

       

       

THEN the whole area is bh, which is for both triangles, so just one is ½ × bh.

   

Source: https://www.mathsisfun.com/triangle.html

 

PDF/Worksheet Links:

  1. Classifying Trianlges https://cdn.kutasoftware.com/Worksheets/Geo/4-Classifying%20Triangles.pdf
  2. http://www.homeschoolmath.net/worksheets/table-classify-triangles.php?problemtype=1&imagesize=1&col=3&row=5&workspace=0&orientation=portrait&font=Arial&FontSize=12pt&pad=10&border=on&ptitle=&PDF_worksheet=1
  3. http://www.homeschoolmath.net/worksheets/table-classify-triangles.php?problemtype=2&imagesize=1&col=3&row=5&workspace=0&orientation=portrait&font=Arial&FontSize=12pt&pad=10&border=on&ptitle=&PDF_worksheet=1
  4. http://www.homeschoolmath.net/worksheets/table-classify-triangles.php?problemtype=3&imagesize=1&col=3&row=5&workspace=0&orientation=portrait&font=Arial&FontSize=12pt&pad=10&border=on&ptitle=&PDF_worksheet=1
  5. http://www.homeschoolmath.net/worksheets/table-classify-triangles.php?problemtype=3&imagesize=2&col=3&row=3&workspace=0&orientation=landscape&font=Arial&FontSize=12pt&pad=10&border=on&ptitle=&PDF_worksheet=1
  6. Isosceles and Equilateral Triangles http://www.baschools.org/vimages/shared/vnews/stories/5226788fe3aae/4-6%20Worksheet%20Brook%20updated%20pdf.pdf
  7. Interior and Exterior Angles https://www.iss.k12.nc.us/cms/lib4/NC01000579/Centricity/Domain/4181/SAS%20FollowUpWorksheet_HW.pdf
  8. Triangles and Pythagoras https://jayoub101.files.wordpress.com/2012/02/triangles-and-pythagoras.pdf
  9. https://d3jc3ahdjad7x7.cloudfront.net/1alyzYql6mrTIPkb1m6r1eShkeb6v1ycjHW94rkJ90Td4ckD.pdf
  10. Triangle Proofs
  11. http://ahs.arabcityschools.org/ourpages/auto/2013/1/14/57509334/Triangle%20Proofs%20Review%201_14_13.pdf

 

Video Links:

  1. Area and Perimeter of a Triangle https://www.youtube.com/watch?v=-psau4jgyaI      
  2. Measurement for Similar Triangles https://youtu.be/eFEkVOi-WhI
  3. https://youtu.be/kjsY8NzzKdQ
  4. https://youtu.be/ixMQGNDriZI
  5. Proof that a Triangle is 180 degrees https://youtu.be/43ZlSjnpE5M
  6. Similar Triangles https://youtu.be/YeOvQl-xzaY