Congruence and Similarity

Introduction to Congruence

Transformations and Congruence

Methods for Enlargements

Enlargements, Ratio and Scale Factors

Introduction to Similarity

Transformations and Similarity

Similarity in Triangles

Using similarity proportion to solve problems

Trigonometry and Similarity

Applying Similar Triangles (Investigation)

Applications of Similarity and Symmetry

Area and Volumes of Similar Figures

Level 6 - NCEA Level 1

Applications of Similarity and Symmetry

Interactive practice questions

A stick of height $1.1$1.1 m casts a shadow of length $2.2$2.2 m. At the same time, a tree casts a shadow of $6.2$6.2 m.

The tree that has $h$h $m$ height casts a shadow of $6.2$6.2 $m$ long. At the same time, a stick with $1.1$1.1 $m$ height casts a shadow of $2.2$2.2 $m$ long. When connecting the top of the tree to the tip of its shadow, it forms a right triangle. Also, when connecting the tip of the stick to the tip of its shadow, it forms a right triangle. These two triangles formed are similar due to the side that is represented by the heights of stick and tree correspond to each other. Sides representing the lengths of their shadows are corresponding sides.

If the tree has a height of $h$h metres, solve for $h$h.

Easy

1min

A $4.9$4.9 m flagpole casts a shadow of $8.6$8.6 m. $Amelia$ casts a shadow of $2.5$2.5 m.

If $Amelia$ is $h$h metres tall, solve for $h$h correct to one decimal place.

Easy

1min

$James$ is $1.7$1.7 m tall and casts a shadow $2$2 m long. At the same time, a tower casts a shadow $13$13 m long. If the tower is $h$h metres high, solve for $h$h correct to one decimal place.

Easy

1min

Outcomes

GM6-5

Recognise when shapes are similar and use proportional reasoning to find an unknown length

91031

Apply geometric reasoning in solving problems

What is Mathspace

About Mathspace