18
QuizMultiple Choice

Congruent and Similar Triangles in the Coordinate Plane

Question 18 • *CR CCSS Math 2 S2 [M2960OX]

The side lengths of triangle ABC are 3, 4, and 5. Which set of ordered pairs form a triangle that is congruent to triangle ABC?

Answer
A
(−3,1),(−3,5),(0,5)
B
(1,−2),(1,3),(4,3)
C
(6,−3),(1,−3),(6,1)
D
(1,3),(1,4),(5,1)

Explanation

A triangle with side lengths 3, 4, and 5 is a right triangle. In choice A, the points (−3,1) and (−3,5) are 4 units apart, and (−3,5) and (0,5) are 3 units apart; these sides meet at a right angle. The third side is √(4² + 3²) = 5, so this triangle has the same side lengths as triangle ABC and is congruent to it.

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