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Geometry

Congruent and Similar Triangles

Triangles - Identify 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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