EasyMathematicsHigh School (9–10)GeometryConceptual

Triangle ABC is congruent to triangle PQR, with the corners matching in the order written…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Triangle $ABC$ is congruent to triangle $PQR$ , with the corners matching in the order written. In triangle $ABC$ , $AB = 8\ \text{cm}$ , $BC = 5\ \text{cm}$ and $\angle B = 74^\circ$ . Find $PQ$ , $QR$ and $\angle Q$ .

Need a reminder? The key ideaShow

Triangles are congruent when they fit exactly on each other. In $\triangle ABC \cong \triangle PQR$ the order of the letters shows which corners match, and by CPCT every matching side and angle is equal. SAS needs two sides and the angle between them. A common side is equal to itself.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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