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Determine if the triangles, △NHQ and △YHZ, are similar. If so, identify the similarity criterion.

Determine if the triangles, △NHQ and △YHZ, are similar. If so, identify the similarity-example-1
User Julius Printz
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1 Answer

17 votes
17 votes

Answer:

Yes. The triangles are similar

Similarity criterion:

Angle H is shared and the side lengths are in a common ratio.

The similarity statement: SSS

Step-by-step explanation:

We know by looking at the triangle that the angle H is shared by both △NHQ and △YHZ. Furthermore, the side lengths of the triangle are in common ratio, meaning

HQ = 2* HZ

HN = 2* HY

QN = 2 * YZ

therefore by SSS, we conclude that the triangles △NHQ and △YHZ are similar.

Note: as a general rule, if any two triangles have all three sides in common ratio, then they are by SSS similar triangles.

User Jeff Storey
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