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Year 7AC9M7SP02

Classifying Triangles and Quadrilaterals

Classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships.

Shapes are named by their sides and their angles. Sorting them properly also means accepting that one shape can have several correct names.

Method

Triangles by sides
equilateral, isosceles, scalene\text{equilateral, isosceles, scalene}
Three equal, two equal, none equal.
Triangles by angles
acute, right, obtuse\text{acute, right, obtuse}
A triangle has both a side name and an angle name.
Quadrilaterals overlap
A square is also a rectangle, a rhombus and a parallelogram. All at once.

Worked example

e.g. Name a triangle with sides 5,5,8 and a largest angle of 106∘.\text{Name a triangle with sides } 5,5,8 \text{ and a largest angle of } 106^\circ.
  1. Compare the sides.5=5≠8two equal5 = 5 \neq 8 \quad \text{two equal}
  2. Give the side name.isosceles\text{isosceles}
  3. Look at the largest angle.106∘>90∘106^\circ > 90^\circ
  4. Give the angle name.obtuse\text{obtuse}
  5. Put both names together.an obtuse isosceles triangle\text{an obtuse isosceles triangle}

Practice

Give both a side name and an angle name where you can.

1
Sides 6,6,6\text{Sides } 6,6,6
Answerequilateral (and acute)\text{equilateral (and acute)}
2
Angles 90,45,45\text{Angles } 90,45,45
Answerright-angled isosceles\text{right-angled isosceles}
3
A quadrilateral with 4 equal sides and 4 right angles\text{A quadrilateral with 4 equal sides and 4 right angles}
Answersquare\text{square}
4
Is every rectangle a parallelogram?\text{Is every rectangle a parallelogram?}
AnswerYes — both pairs of opposite sides are parallel.\text{Yes — both pairs of opposite sides are parallel.}
5
Is every parallelogram a rectangle?\text{Is every parallelogram a rectangle?}
AnswerNo — the angles need not be 90∘.\text{No — the angles need not be } 90^\circ.
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