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Geometry

Classification of Triangles

Concept Quizzes

Classification of Triangles Warmup
Triangles - Classification By Angles
Triangles - Classification by Sides
Properties of Equilateral Triangles
Properties of Isosceles Triangles

Challenge Quizzes

Classification of Triangles: Level 1 Challenges
Classification of Triangles: Level 2 Challenges
Classification of Triangles: Level 3 Challenges

Triangles - Classification by Sides

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

17 11 8 14

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by Brilliant Staff

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

16 13 10 7

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

\displaystyle { {162} \leq \lvert \overline {BC} \rvert < {202} }

\displaystyle { {160} \leq \lvert \overline {BC} \rvert < {200} }

\displaystyle { {164} \leq \lvert \overline {BC} \rvert < {204} }

\displaystyle { {166} \leq \lvert \overline {BC} \rvert < {206} }

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

{72}\sqrt{2}

{108}

{86}

{74}\sqrt{3}

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

51 49 52 50

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by Brilliant Staff