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Triangle Types Comparison

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Triangle Types Comparison

A park in Aotearoa New Zealand is adding triangular signs to a walking trail. Use side lengths and angle facts to identify, compare and sketch triangles. A triangle may have both a side-based name and an angle-based name.

Read the design notes

The trail team records three side lengths and one angle fact for each sign design. All measurements are in centimetres.

Design

Side lengths

Angle information

A

5, 5, 5

All angles are 60°

B

5, 5, 8

No angle is 90°

C

3, 4, 5

One angle is 90°

D

4, 6, 7

All angles are less than 90°

Classify and compare

Use the design notes above. Remember: equilateral, isosceles and scalene describe side lengths; acute, right-angled and obtuse describe angles.

1.Which design is equilateral? Explain how its side lengths show this.
2.Choose the best side-based name for design B.
  • Equilateral
  • Isosceles
  • Scalene
  • Right-angled
3.Design C has one right angle. What is its angle-based name, and what is its side-based name?
4.True or false: design A is also an acute triangle. Give a reason.
TrueFalse
5.Complete the rule: A triangle with three different side lengths is called a triangle.
6.Which design notes let you know that design D is acute? What does acute mean?
7.Select every statement that is true for all triangles.
  • They have three sides.
  • Their interior angles add to 180°.
  • They have at least one right angle.
  • They have three vertices.
  • All three sides are equal.
8.Compare designs A and B. State one similarity and one difference in their side lengths.

Sketch a new sign

Create your own triangle sketches. Mark equal sides with matching tick marks and show any right angle with a small square corner.

9.Draw an isosceles triangle that is not equilateral. Add tick marks to show which sides are equal, then label it with its side-based name.
10.Design a right-angled triangle that is also isosceles. Draw it, mark the right angle and show the pair of equal sides. Why can one triangle have both names?

2 printable pages

  • Triangle Types Comparison, page 1 of 2: Read the design notes, Classify and compare

    Page 1

  • Triangle Types Comparison, page 2 of 2: Sketch a new sign

    Page 2

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