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# Congruent and Similar Triangles

If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.

# 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?

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.

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

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?

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 $$\overline{AB}$$?

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