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Congruent and Similar Triangles

If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.

Identifying Similar Triangles

         

In the above diagram, if \(a=18,\) \(b=12,\) \(c=14\) and \(d=8,\) what is the measure of \(\overline{AD} ?\)

Note: The above diagram is not drawn to scale.

Given \(\triangle PQR\) with side lengths \(\lvert{\overline{PQ}}\rvert=16\text{ cm},\) \(\lvert{\overline{QR}}\rvert=20\text{ cm}\) and \(\angle PQR=60^\circ,\) which of the following triangles is similar to \(\triangle PQR ?\)

(a) \(\triangle ABC\) with side lengths \(\lvert{\overline{AB}}\rvert={15}\text{ cm},\) \(\lvert{\overline{AC}}\rvert={12}\text{ cm}\) and \(\angle BAC=60^\circ\)
(b) \(\triangle DEF\) with side lengths \(\lvert{\overline{DE}}\rvert={8}\text{ cm},\) \(\lvert{\overline{DF}}\rvert={10}\text{ cm}\) and \(\angle EDF=80^\circ\)
(c) \(\triangle GHI\) with angles \(\angle GHI=60^\circ\) and \(\angle GIH=80^\circ\)
(d) \(\triangle JKL\) with side lengths \(\lvert{\overline{JK}}\rvert={20}\text{ cm},\) \(\lvert{\overline{KL}}\rvert={18}\text{ cm}\) and \(\lvert{\overline{JL}}\rvert={16}\text{ cm}\)

In the above diagram, \(x=21,\) \(y=14,\) \(\alpha={35}^\circ,\) and \(\beta={75}^\circ.\) Which condition would mean that the two triangles are similar?

Note: The above diagram is not drawn to scale.

In the above diagram, if \(a=30,\) \(b=25\) and \(\angle BAC=\angle AHC=90^\circ,\) what is the measure of \(\overline{HC} ?\)

Note: The above diagram is not drawn to scale.

In the above diagram, if \(a=45,\) \(b=30\) and \(\angle ABC=\angle DAC,\) what is the measure of \(\overline{BD} ?\)

Note: The above diagram is not drawn to scale.

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