Congruence and Similarity practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise congruence and similarity free

What this topic covers

Congruent Figures
Scale Drawings and Maps
Similar Triangles

Worked examples

Example 1

A model has a scale of

1 : 2000

. The base of the model has an area of

4

cm². Find the actual area of the base in m².

Show the worked solution

$1 \text{ cm represents } 2000 \text{ cm} = 20 \text{ m} \quad \scriptsize\textit{scale } 1 : 2000$
$\text{Area scale factor} = 20^2 = 400 \quad \scriptsize\textit{area scale is square of length scale}$
$\text{Actual area} = \text{model area} \times \text{area scale factor}$
$= 4 \times 400$
$$= 1600$ m²$

Answer: $1600$

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.