Year 10: Congruent triangles

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Congruent triangles have exactly the same size and shape. In Year 10, you need to decide whether two triangles are congruent and then use that fact to find unknown sides and angles.

Useful congruence tests

• $\text{SSS}$: three matching sides.
• $\text{SAS}$: two matching sides and the included angle.
• $\text{AAS}$ or $\text{ASA}$: two matching angles and one side.
• $\text{RHS}$: right angle, hypotenuse, and one side.

Matching the triangles carefully

Always work out which vertex matches which vertex before writing conclusions. The order matters when you name the congruent triangles.

Finding unknown values

Once congruence is established, transfer the known side or angle from one triangle to its matching partner.

Reading diagrams carefully

Tick marks on sides and arcs on angles usually show correspondences. If two equal sides meet an equal angle, the $\text{SAS}$ test is often the correct one to use.

Common mistakes

• Using $\text{SSA}$, which is not a general congruence test.
• Matching the wrong vertices.
• Assuming triangles are congruent just because they look similar on a sketch.

Study routine

Mark equal sides and angles, decide which congruence rule fits the information, then state what matching parts are equal. That sequence is clear and exam-friendly.

Skills to practise

• Congruent triangles