Question

AB = 15, BC = 10, and CD= 7. Find the length DA.

451. Equilateral triangles BCP and CDQ are attached to the outside of regular pentagon
ABCDE. Is quadrilateral BPQD a parallelogram? Justify your answer.

Answer 1

451. No, the angles are wrong.

Explanation:

450. AB = 15, BC = 10, and CD= 7. Find the length DA.

This cannot be done without additional information about the sort of figure that ABCD is. If these are points on a line segment, we need to know their order. If these are points on a quadrilateral, we need to know its description in more detail.

If these are points ordered ABCD on a line, then AD = 15+10+7 = 32.

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451. See the attached figure. BPQD is not a parallelogram: BCQ is not a straight line. (The internal angles of a pentagon are 108°, but would need to be 120° for BCQ to be a straight line, making BP parallel to DQ.) Instead, BPQD is an isosceles trapezoid.