Triangle Congruence: ASA and AAS — Quiz

Question 6 • Geometry

Which of these triangle pairs can be mapped to each other using two reflections?

Answer

Image with description Triangles X Y Z and Z A T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle Z A T. Side X Z is congruent to Z T. Angles Z A T, and X Y Z are right angles. Angle X Z Y is congruent to Z T A.

Image with description Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.

Image with description Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T. Side X Z is congruent to side P T, angle X Y Z is congruent to angle T Y P, and angle X Z Y is congruent to angle Y T P.

Image with description Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.

Explanation

A reflection reverses orientation, and doing two reflections produces an orientation-preserving transformation. Choice B describes exactly two reflections: first across XY, then across YZ, mapping triangle XYZ to triangle PYT. The other choices describe an odd number of reflections combined with rotations or shifts, which reverse orientation.

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