Geometry

Congruent and Similar Triangles

Similar Triangles Problem Solving

         

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

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

AE=2EB,BM=4,AD=6,BC=9, \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 AE\lvert\overline{AE}\rvert denotes the length of AE.\overline{AE}. What is DO?\lvert\overline{DO}\rvert?

Note: The above diagram is not drawn to scale.

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

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

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