# Write a similarity statement relating the three triangles in the diagram.12210107051.jpg

Write a similarity statement relating the three triangles in the diagram.

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Step 1
$In\mathrm{△}NOP\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}NQO$
1) $\mathrm{\angle }ONP\stackrel{\sim }{=}\mathrm{\angle }QNO$ (same angle)
2)$\mathrm{\angle }PON\stackrel{\sim }{=}OQN$ (right angles)
So, $\mathrm{△}NOP\sim \mathrm{△}NQO$ (by AA property)
Step 2
$In\mathrm{△}NOP\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}OQP$
1)$\mathrm{\angle }OPN\stackrel{\sim }{=}\mathrm{\angle }OPQ$ (same angle)
2)$\mathrm{\angle }PON\stackrel{\sim }{=}\mathrm{\angle }PQO$ (right angle)
So, $\mathrm{△}NOP\sim \mathrm{△}OQP$ (by AA property)
So, $\mathrm{△}NOP\sim \mathrm{△}OQP\sim \mathrm{△}NQO$
Result:$\mathrm{△}NOP\sim \mathrm{△}OQP\sim \mathrm{△}NQO$.