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Classification of Triangles

Triangles - Classification by Sides


If the above triangle is an equilateral triangle and the length of AB\overline{AB} is AB=11, \lvert \overline {AB} \rvert =11 , what is AC? \lvert \overline {AC} \rvert ?

If ABC \triangle ABC is a right triangle and the lengths of two sides are AB=6 \lvert \overline {AB} \rvert = 6 and AC=8,\lvert \overline {AC} \rvert = 8 , what is BC? \lvert \overline {BC} \rvert ?

ABC \triangle {ABC} is an acute triangle with side lengths AB=120 \lvert \overline {AB} \rvert = 120 and AC=160.\lvert \overline {AC} \rvert = 160. If BCAC,\lvert \overline {BC} \rvert \geq \lvert \overline {AC} \rvert, what is the possible range of BC? \lvert \overline {BC}\rvert?

Solid figure ABCDEFGHABCDEFGH is a regular cube with side length 12. 12. What is the area of DEF? \triangle DEF ?

Angle A\angle A is an obtuse angle in triangle ABCABC with side lengths AB=30 \lvert \overline {AB} \rvert = 30 and AC=40.\lvert \overline {AC} \rvert = 40. If BC\lvert \overline {BC} \rvert is an integer and BCAC,\lvert \overline {BC} \rvert \geq \lvert \overline {AC} \rvert, what is the minimum value of BC?\lvert \overline {BC}\rvert ?


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