Year 8 Maths • AC9M8SP01 • Authored homework
Congruence and similarity
Practise Congruence and similarity through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.
Part A
Short-answer questions
State the SSS, SAS, ASA or RHS condition for congruent triangles.
Decide whether triangles with sides 5, 7, 8 and 5, 7, 8 are congruent.
Find the scale factor from a triangle with side 4 cm to a similar triangle with matching side 10 cm.
A student says equal area proves two triangles are congruent. Correct the claim.
Write the rule or formula most useful for Congruence and similarity.
Show how to check one answer using estimation, substitution or inverse operations.
Write one common mistake students make in Congruence and similarity and correct it.
Create a small table, diagram or equation that represents this topic.
State where units, exact form or rounding matter in this topic.
Write one exam-style short question on Congruence and similarity and solve it.
Part B
Long-answer questions
Use similarity to find a missing side when two matching sides are 6 cm and 15 cm.
Prove two triangles are congruent using a labelled diagram and a valid congruence condition.
Solve a multi-step problem involving Congruence and similarity and explain every step clearly.
Create a realistic word problem for Congruence and similarity, solve it and interpret the answer.
Compare two methods for a problem in Congruence and similarity and explain which is more efficient.
Write a worked solution that includes a check for reasonableness.
Create a problem with a deliberate trap, then solve it correctly and explain the trap.
Use a diagram, table, graph or equation to model a situation involving Congruence and similarity.
Explain how this topic connects to a previous Year 7 or Year 8 maths skill.
Write a full-mark response to a challenging Congruence and similarity question, including reasoning and final answer.
Part C
Research and understanding task
Research a real use of similarity or congruence in maps, shadows, design or construction. Explain it with a diagram.