Geometry

Congruent and Similar Triangles

Triangles - Identify Similar Triangles

         

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

Note: The above diagram is not drawn to scale.

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

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

In the above diagram, x=21,x=21, y=14,y=14, α=35,\alpha={35}^\circ, and β=75.\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,a=30, b=25b=25 and BAC=AHC=90,\angle BAC=\angle AHC=90^\circ, what is the measure of HC?\overline{HC} ?

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

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