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

Answer 1

two triangle may be congruent but additional information is needed about the angle measures.



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Answer 2

The given two triangles are congruent But differently oriented.

Explanation:

• Let the Rectangle be denoted by ABCD with its vertices A, B, C, and D respectively.
• Then the line joining the two corners is the diagonal AC.
• The diagonal AC divides the rectangle into two triangles ABC and ADC.
• Given that AC divides the angle A and C into two angles of $32\ and\ 58$ degrees.
• Here, the triangles are right-angled triangles.
• Therefore in triangles ABC and ADC,  $\angle D=\angle B= 90 \ \ \ \ \ \ \ \ \ \ \ \ \ (Angles\ of\ rectangle)\\ \angle DAC=\angle BCA=32\\\angle ACD=\angle CAB=58\\AB=DC,\ AD=BC\ \ \ \ (Opposite\ sides\ of\ rectangle)\\ AC \ \ \ \ (common\ side)$        
• Hence both the triangles will have equal sides and angles but are oriented differently.