Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Triangle ABC has sides cm, cm and cm. Triangle PQR has sides cm, cm and cm. Show that the triangles are similar. Take AB and PQ as the shortest sides, and find the ratio .
Two triangles are similar if two angles of one equal two angles of the other (AA). They are also similar if their three side ratios are equal (SSS), or if one angle is equal and the sides around it are in the same ratio (SAS). Write similar triangles with their letters in matching order, and match the sides in that order: .
Have you tried it?
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.
Step 1. Match the sides. Shortest with shortest, middle with middle and longest with longest: , and .
Step 2. The ratios. , and .
Step 3. Conclude. The three ratios are equal, so by SSS.
Answer: the triangles are similar, and .
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