State whether the following shapes are concave (non-convex) or convex:
Draw an example of:
A convex regular pentagon.
A concave seven-sided polygon.
Classify the following triangles as scalene, isosceles or equilateral:
State whether the following triangles are equilateral:
State whether the following shapes are kites:
Is the following figure a kite? Explain your answer.
State whether the following are parallelograms:
State whether the following are rectangles:
Classify the following as a rectangle or square:
Determine whether the following is either a rhombus, parallelogram or kite:
Classify the following quadrilaterals using all the terms that apply out of:
rectangle, rhombus, kite, parallelogram.
State whether each the following statements is true:
A square is a rhombus.
A trapezium is a parallelogram.
A parallelogram is a rectangle.
A kite is a rhombus.
A rhombus is a square.
State whether the following shapes have two pairs of opposite parallel sides:
Trapezium
Rectangle
Parallelogram
Kite
Answer the following questions.
For each polygon with the given number of sides, complete with its number of diagonals:
| \text{Number of Sides (n)} | 4 | 5 | 6 |
| \text{Number of Diagonals (d)} |
The number of diagonals d in an n-sided polygon is given by the formula d = \dfrac{n^{2} - 3 n}{2} .
Use the formula to find the number of diagonals in a 10-sided polygon.
Consider the non-convex hexagon:
What is the least number of triangles that it can be divided into?
What is the interior angle sum of the non-convex hexagon?
Consider the convex hexagon:
Find the least number of triangles that the hexagon can be divided into.
Find the interior angle sum of the hexagon.
Consider the pentagon:
Find the value of the following:
Deduce the angle sum of the pentagon.
How many non-overlapping triangles can an n-sided figure be split into?
Determine whether each of the following is the rule for the angle sum of an n-sided polygon:
Consider the figure. The quadrilateral is divided into two triangles (this is the least number of triangles that a quadrilateral can be divided into).
The interior angle sum of a quadrilateral is therefore equal to double the interior angle sum of a triangle.
Complete the following table. 'Least Number of Triangles' means the least number of triangles that the shape can be divided up into.
| Number Of Sides | Least Number of Triangles | Interior angle sum | |
|---|---|---|---|
| Pentagon | |||
| Hexagon | |||
| Heptagon | |||
| Octagon | |||
| Nonagon | |||
| Decagon |
Find the sum of the interior angles in the following figures:
Quadrilateral
Twelve-sided polygon
Fourteen-sided polygon
Sixteen-sided polygon
Twenty-sided polygon
Forty-sided polygon
For each of the following figures:
Find the value of y.
Find the value of x.
Find the value of y in the following figure:
Consider an octagon.
What is the sum of its interior angles?
Given that it is regular, find the size of each interior angle.
For each of the following regular polygons, find the value of x:
For each of the following polygons:
Find n, the number of sides.
Classify the polygon.
A polygon with equal internal angles of 120 \degree.
A polygon with equal internal angles of 135 \degree.
A polygon with equal internal angles of 60 \degree.
Explain why a regular polygon with equal internal angles of 50 \degree is not possible.
Find the interior angle sum of a regular polygon whose exterior angles measure 40 \degree.
The sum of the interior angles of a regular 8-sided shape is 1080 \degree. Find the size of each interior angle.
Consider the given quadrilateral:
Find the value of:
What property about quadrilaterals has been shown?
Consider the following figure:
Find the value of y.
Find the value of x:
Find the size of one exterior angle for the following regular polygons:
Pentagon
Octagon
Triangle
Nonagon
Find the size of one interior angle for the following regular polygons:
Hexagon
Quadrilateral
Decagon
Twelve-sided polygon