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Geometry

Congruent and Similar Triangles

Concept Quizzes

Similar and Congruent Triangles Warmup
Triangles - Identify Congruent Triangles
Triangles - Identify Similar Triangles
Triangles - Compare Similar Triangles
Similar Triangles Problem Solving

Challenge Quizzes

Congruent and Similar Triangles: Level 1 Challenges
Congruent and Similar Triangles: Level 2 Challenges
Congruent and Similar Triangles: Level 3 Challenges

Triangles - Compare Similar Triangles

In the above triangle, point D divides $\overline{AB}$ in the ratio $\ 2:1$ and point E divides $\overline{AC}$ in the ratio $\ 1:2.$ If the area of $\triangle ABC$ is $23,$ what is the area of $\triangle ADE?$

\frac{92}{9}

\frac{46}{9}

\frac{46}{3}

\frac{23}{4}

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by Brilliant Staff

Triangle $\triangle ABC$ is similar to $\triangle DCE$ with $\overline{AB} \parallel \overline{CD}.$ If the area of $\triangle ABC$ is $36$ and the area of $\triangle DCE$ is $9,$ what is the area of $\triangle ACD?$

Note: The above diagram is not drawn to scale.

13 23 21 18

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by Brilliant Staff

$\overline{AB}$ is parallel to $\overline{DE}$ , the length of $\overline{AC}$ is $3,$ and the length of $\overline{CD}$ is $11.$ If the area of $\triangle ABC$ is $4,$ what is the area of $\triangle CDE$ ?

Note: The above diagram is not drawn to scale.

\frac{484}{9}

\frac{44}{3}

\frac{36}{121}

\frac{12}{11}

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by Brilliant Staff

Triangle $\triangle ABC$ is similar to $\triangle DEF$ , and the ratio of their areas is $9:25.$ If the length of $\overline{DE}$ is $70,$ what is the length of $\overline{AB}$ ?

35 63 49 42

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by Brilliant Staff

$\overline{BC}$ is parallel to $\overline{DE}$ , the length of $\overline{AD}$ is $7,$ and the length of $\overline{BD}$ is $3.$ If the area of $\triangle ABC$ is $17,$ what is the area of $\triangle ADE$ ?

Note: The above diagram is not drawn to scale.

\frac{119}{10}

\frac{833}{100}

\frac{119}{3}

\frac{51}{7}

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by Brilliant Staff