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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

Congruent and Similar Triangles: Level 1 Challenges

In triangles $ABC$ and $DEF$ , if we know that $AB = EF, BC = DE$ and $\angle ABC = \angle DEF$ , are the triangles congruent?

Not necessarily so They are always congruent They can never be congruent

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by Calvin Lin

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In the above diagram, $x=21,$ $y=14,$ $\alpha={35}^\circ,$ and $\beta={75}^\circ.$ Which condition would mean that the two triangles are similar?

Note: The above diagram is not drawn to scale.

\lvert\overline{AB}\rvert=18, \lvert\overline{DE}\rvert=12

\lvert\overline{AC}\rvert=19, \lvert\overline{DE}\rvert=12

\lvert\overline{AB}\rvert=19, \lvert\overline{DF}\rvert=18

\angle A=\angle D=70^\circ

\angle C=70^\circ, \angle F=30^\circ

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by Gene Keun Chung

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In the adjoining figure, $XY$ is parallel to $AC$ . If $XY$ divides the triangle into two halves with equal area, compute $\dfrac{AX}{AB}$ .

\frac{1}{\sqrt{2}}

\frac{\sqrt{2}+1}{\sqrt{2}}

\frac{\sqrt{2}-1}{\sqrt{2}}

\frac{1}{2}

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by Rayyan Shahid

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Did you know you can approximate the diameter of the moon with a coin $($ of diameter $d)$ placed a distance $r$ in front of your eye?

If the distance between the moon and your eye is $R,$ what is the diameter of the moon?

\frac{R}{dr}

\frac{r}{R}d

\frac{R}{d}r

\frac{R}{r}d

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by Lakshan Dumpa

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Triangle $\triangle ABC$ is similar to $\triangle DEF$ , and the ratio of their areas is $9:25.$ If the length of $\overline{DE}$ is $60,$ what is the length of $\overline{AB}$ ?

42 30 54 36

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by Perry Ellis

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