Congruent and Similar Triangles

Congruent and Similar Triangles: Level 1 Challenges


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

In the above diagram, x=21,x=21, y=14,y=14, α=35,\alpha={35}^\circ, and β=75.\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, XYXY is parallel to ACAC. If XYXY divides the triangle into two halves with equal area, compute AXAB\dfrac{AX}{AB} .

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

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

Triangle ABC\triangle ABC is similar to DEF\triangle DEF, and the ratio of their areas is 9:25.9:25. If the length of DE\overline{DE} is 60,60, what is the length of AB\overline{AB} ?


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