5
QuizMultiple Choice

Congruence

Question 5 • (AG Q4) Math 8: 25-26 (JTurner)

Linnea has drawn a line from one corner of a rectangle to the opposite corner. The line divides each of the right angles into two angles of measures 32° and 58°. Which statement best describes the resulting triangles?

Answer
A
The two triangles are not congruent because the corresponding sides do not have the same length.
B
The two triangles are congruent but are oriented differently.
C
The two triangles may be congruent, but additional information is needed about the angle measures.
D
The two triangles may be congruent, but additional information is needed about the side lengths.

Explanation

The diagonal divides the rectangle into two triangles. Opposite sides of a rectangle have equal lengths, and the triangles share the diagonal, so their three corresponding sides are equal; therefore, the triangles are congruent. They are oriented differently within the rectangle, so B, “The two triangles are congruent but are oriented differently,” is correct.

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