Triangle Basics
How many sides does a triangle have?
3 sides
This tool is used to measure angles.
Protractor
If all three angles are given as 60°, what kind of triangle can you draw?
Equilateral
Sketch a triangle with angles 90°, 45°, and 45°. What kind of triangle is it?
Right isosceles triangle
Three side lengths are 4, 5, and 6. How many triangles can you make?
Unique Triangle/One Triangle
What is the sum of the interior angles of any triangle?
180 degrees
This tool is used to draw straight lines.
Ruler
True or False: If all three sides are given and follow triangle inequality, only one triangle can be drawn.
TRUE
If you're given sides of 6 cm, 8 cm, and 10 cm, what type of triangle should you sketch?
Right Triangle
Sides: 2 cm, 2 cm, and 5 cm. How many triangles can you make?
None
Name the triangle with all equal sides.
Equiateral triangle
What tool is used to help us draw circles.
Compass
Can you always draw a triangle with sides 3 cm, 4 cm, and 10 cm?
No
Given sides of 3 cm, 3 cm, and 4 cm, draw and name the triangle.
Isoscles triangle
Sides: 2 cm, 2 cm, and 5 cm. How many triangles can you make?
More than one
True or False: A triangle can have two right angles.
FALSE
This method allows for easy trial-and-error sketching.
Freehand drawing
If you're given two side lengths and one angle not between them, can more than one triangle be formed?
Yes
Sketch a triangle with sides 5 cm, 5 cm, and 10 cm. What do you notice?
A straight line or no triangle — the sides do not meet the triangle inequality rule?
Given three angles: 30°, 60°, and 90°, can you make a unique triangle?
No — infinitely many similar triangles, but not a unique one in size. No
What kind of triangle has two equal sides and one different side?
Isosceles triangle
Explain how to draw an angle with a protractor.
1. Plot the vertex
2. Plot a line toward the angle
3. Connect the two points
4. Draw the base line
5. Label the angle
What is the triangle inequality theorem?
What is the rule that the sum of any two sides must be greater than the third side?
You are given side lengths of 7 cm, 2 cm, and 4 cm.
Try to sketch the triangle. Can a triangle be formed with these side lengths? Why or why not?
No, a triangle cannot be formed because the sum of the two shorter sides (2 cm + 4 cm = 6 cm) is less than the longest side (7 cm).
This violates the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
All three sides are the same length. How many triangles can you make?
What is one unique equilateral triangle?