Explore Triangles and Quadrilaterals | Instructions: | Suggested Lessons or Activities: | Other Related Modules and Useful Links:

Explore Triangles and Quadrilaterals

© R. Mirshahi


  • Click and drag the red circles at the corners of the shapes to create a different shape. You can measure the area and the perimeter of any shape using the grid or the ruler.

Suggested Lessons or Activities:

  • Use the triangle tool to study different types of triangles (e.g., right-angle, scalene, isosceles, equilateral). Look at them below:

Equilateral Triangle_1.jpg isosceles triangle01.jpg Right-Angled Triangle01.jpg scalene triangle_01.jpg

All sides and angles are equal in the equilateral triangle.
2 sides and 2 angles are equal in the isosceles triangle.
The right-angled triangle (right triangle) has one angle that is 90 degrees.
A scalene triangle has no equal sides nor angles.

  • Use the quadrilateral tool to study different types of quadrilaterals (e.g., square, rectangle, rhombus, parallelogram, trapezoid, kite, etc.). Discuss what makes these shapes special. How are they similar and different from each other. For example you can ask:
  1. Start with any triangle with a horizontal base and move its top vertex horizontally to show that all the resulting triangles will have the same area (equal lengths and heights).
  2. Make a trapezoid with a specific area.
  3. Make a right-angled trapezoid. What do you notice?
  4. Drag one corner of a square to make a kite.
  5. Make a rectangle and explain how you can change it to a parallelogram with no right angles. How can you prove this shape is a parallelogram?
  6. Make a rhombus with no right angles.
  7. For example, how many pairs of parallel lines does a square have? Use the ruler to test if two sides are parallel. You can also determine if two lines are parallel by calculating their slope (m) by using this formula: Slope = y2-y1 / x2-x1 (rise over run).

  8. How many right angles does a rectangle have?
  9. How many right angles can a trapezoid have?
  10. Why is a square considered a special rhombus?
  11. Which shapes have lines of symmetry?
  12. Advanced users:
* Use the Pythagorean Theorem to determine the length of a diagonal side (hypotenuse) of a right triangle on the grid (The square root of the sum of the squares of the other two sides that are on the grid). Here is a simple application of Pythagorean theorem.
Pythagorean theorem345.PNG
  • You can overlap all the corners to model a single point (no dimensions). Then move the top point to show how the distance between two points is a straight line (one-dimensional) and by moving the third point we have a triangle which is a 2-dimensional shape
  • Study x and y coordinates
  • Study simple trigonometry. You can use the interactive ruler and protractor to study familiar trigonometric functions such as the sine, cosine, and tangent.
  • demonstrate the 3:4:5 triangle and the Pythagorean triples. The 3:4:5 triangle is used by carpenters as well as people in construction to create square angles (90 degrees) without doing any calculations. To make a perfect square angle, all you need is a piece of string!!!

Hands-on Activities (Extension)

You can create a perfect square and an equilateral triangle.
-Fold the rectangular paper into a square and cut the square out (step 1-4).

Fractal instructions triangles10001.png

-Fold the square in half to show the line of symmetry (step 5). Fold the bottom corner of the square to find the third point of the equilateral triangle (step 6). Mark this point and draw lines from the bottom corners to this point. This is your equilateral triangle. Cut it out.

Fractal instructions triangles10002.png

How to Create a 30° Angle Without using a Protractor
Any right triangle whose hypotenuse is twice the length of one of the other sides has the following angles: 30°, 60°, and 90°.

  1. Start with a long sheet of legal size paper (ABCD).
  2. The shorter side of the rectangle (AB) will be one of the sides of your triangle.
  3. Using a pair of compasses draw a circle with the radius twice the size of AB with A as the centre. This step can be done with a piece of string if you don't have compasses.
  4. Mark the exact point where the circumference of this circle intersects with BC. This is the third corner of the triangle.

This triangle’s angles are 30°, 60°, and 90°.

How to create a 30 degrees.png
Special Features:
  • full screen
  • all vertices are movable
  • interactive ruler and protractor
  • x and y coordinate grid
  • annotate

Other Related Modules and Useful Links: