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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.

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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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