Topics
12. Geometry
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AustraliaNSW
Stage 3

12.04 Diagonals of shapes

Lesson
Practice
Lesson

Are you ready?

Let's review the  properties of shapes  to help us in this lesson.

Examples

Example 1

How many vertices does each shape have?

a
An image of a rectangle.
Worked Solution
Create a strategy

Count the number of corners of the rectangle where two edges meet.

Apply the idea

Vertices = 4

b
An image of a triangle
Worked Solution
Create a strategy

Count the number of corners of the triangle where two edges meet.

Apply the idea

Vertices = 3

Idea summary

Vertices are the corners where two edges meet.

Diagonals of 2D shapes

This video shows us how to find diagonals in two dimensional polygons.

Loading video...

Examples

Example 2

Consider the following shape.

A pentagon with vertices A, B, C, D, and E
a

What is the name of the shape?

A
Square
B
Trapezium
C
Pentagon
Worked Solution
Create a strategy

Recall the name of shape that has 5 sides or edges.

Apply the idea

Since the shape has 5 sides or edges, the name of the shape is pentagon. So, the correct answer is Option C.

b

How many diagonals does a pentagon have?

Worked Solution
Create a strategy

Draw the diagonals in the pentagon.

Apply the idea

Here is a pentagon with its diagonals drawn on:

A pentagon with vertices A, B, C, D, and E. Its 5 diagonals are drawn.

We can see that the pentagon has 5 diagonals.

Idea summary

A diagonal is a straight line (line segment) that runs between opposite vertices. The vertices can't be adjacent to each other, and we don't count diagonals in the opposite direction separately.

Outcomes

MA3-15MG

manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

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