Question

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?

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.

Answer 1

The correct answer is B. The two triangles are congruent but are oriented differently.

Answer 2

Answer: B. The two triangles are congruent but are oriented differently.

Explanation:

Let ABCD is a rectangle and we draw a line to join vertex A and C such that the line divides each of the right angles into two angles of measures 32° and 58° as in the figure

then in ΔABC and ΔCDA

AB=CD and AD=BC [opposite sides of rectangle are equal]

AC=AC [ reflexive property]

⇒ ΔABC ≅ ΔCDA [SSS congruence criteria]

Thus triangles are congruent but are oriented differently (from the picture)