Congruent and Similar Triangles in the Coordinate Plane

Question 2 • (OC27) MATH COLL LIB ARTS-1207350-S1-Maguire-D'Aquino

Is it possible to create a regular tessellation using a regular decagon? Explain.

Answer

Yes, 2 decagons with a common vertex will have interior angle measures that sum to 360.

Yes, 3 decagons with a common vertex will have interior angle measures that sum to 360.

Yes, all of the angles and sides of each decagon are congruent.

No, a tessellation of 2 decagons will have a gap, and a tessellation of 3 decagons will overlap.

Explanation

A regular decagon’s interior angle is (10 − 2) × 180° ÷ 10 = 144°. Two decagons meeting at a vertex make 288°, leaving a gap of 72°; three make 432°, which is more than 360° and causes overlap. So a regular decagon cannot form a regular tessellation, as choice D states.

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Congruent and Similar Triangles in the Coordinate Plane

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