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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.

# Problem Solving

Let $$\lvert\overline {AB}\rvert$$ denote the length of $$\overline {AB}.$$ Then in the above diagram, $$\lvert\overline {AB}\rvert = \lvert\overline {BC}\rvert$$ and $$\lvert\overline {BF}\rvert = \lvert\overline {FE}\rvert.$$ If $$\lvert\overline{CD}\rvert=38,$$ what is $$\lvert\overline {DE}\rvert?$$

In the above diagram, $$\angle ABD = \angle BCE = \angle CAF.$$ Given the lengths $\lvert \overline{AB}\rvert=12, \lvert \overline{AC}\rvert =7, \lvert \overline{BC}\rvert = 14,$ what is $$\lvert \overline{DE}\rvert : \lvert \overline{EF}\rvert : \lvert \overline{DF}\rvert?$$

Note: The above diagram is not drawn to scale.

In the above quadrilateral $$\square ABCD,$$ $\overline{AD} \parallel \overline{EF} \parallel \overline{BC}, \lvert\overline{AE}\rvert = 2\lvert\overline{EB}\rvert, \lvert\overline{BM}\rvert = 4, \lvert\overline{AD}\rvert = 6, \lvert\overline{BC}\rvert = 9,$ where $$\lvert\overline{AE}\rvert$$ denotes the length of $$\overline{AE}.$$ What is $$\lvert\overline{DO}\rvert?$$

Note: The above diagram is not drawn to scale.

In the above diagram, $$\triangle ABC$$ is a right-angled triangle where $$\angle C$$ is a right angle and $$\lvert{\overline{AC}}\rvert=\lvert{\overline{BC}}\rvert.$$ If $$\lvert{\overline{AC}}\rvert=\lvert{\overline{AD}}\rvert,$$ $$\overline{AB} \perp \overline{DE}$$ and $$\lvert{\overline{CE}}\rvert=7,$$ what is the measure of $$\overline{DB} ?$$

$$\triangle ABC$$ is a right triangle with side lengths $\lvert\overline{AB}\rvert = 25, \lvert\overline{BC}\rvert = 50$ If $$\square{DBEF}$$ in the above diagram is a square, what is the area of $$\square{DBEF}?$$

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