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Geometry

Properties of Triangles

Intro

Concept Quizzes

Properties of Triangles Lightning Quiz
Triangles - Angle Sum
Triangle Inequality
Pythagorean Theorem
Triangles - Calculating Area
Triangles Problem Solving

Challenge Quizzes

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

Pythagorean Theorem

If $x=\sqrt{6}$ and $y=\sqrt{10}$ in right triangle $\triangle ABC$ shown in the diagram above, what is the length of $\overline{AC} ?$

Note: The above diagram is not drawn to scale.

\sqrt{10}-\sqrt{6}

\sqrt{10}+\sqrt{6}

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by Brilliant Staff

Right triangle $ABC$ has side lengths $N+1, N-1,$ and $\frac {N}{2}.$

What is the value of $N?$

15 16 17 18

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by Brilliant Staff

In the figure above, if $l_1=10,$ $l_2=8$ and $\alpha=\beta={56}^\circ,$ what is the value of $x ?$

Note: The above diagram is not drawn to scale.

{4}

{6}

{8}\sqrt{3}

{4}\sqrt{3}

{4}\sqrt{2}

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by Brilliant Staff

As shown in the above diagram, Raj folded a rectangular paper $ABCD$ with side length $\overline{AD} = 5$ in such a way that vertex $D$ falls on side $AB$ and is labeled point $F.$ If the length of $\overline{AF}$ is $2,$ what is the length of $\overline{DE}?$

Note: The above diagram is not drawn to scale.

\frac{3}{10}

\frac{29}{11}

\frac{3}{11}

\frac{29}{10}

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by Brilliant Staff

Dan walks 30 meters east. He then walks 40 meters north. How far (in meters) is he from the starting point?

70 50 55 60

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by Brilliant Staff