Geometry

Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?
A. Quadrilateral ABCD is a square.
B. Quadrilateral ABCD is a rhombus.
C. Quadrilateral ABCD is a rectangle.
D. Quadrilateral ABCD is an isosceles trapezoid.

My first pick is A but A is not the right answer. Correct answer is C. Could someone please explain to me I am confused. Thank you for your help.

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  1. a rectangle is a parallelogram with supplementary opposite angles (and congruent adjacent angles)

    a square is a rectangle with equal sides

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  2. in a parallelogram, adjacent angles are supplementary.

    If they are also congruent, they must be right angles.

    So, C is correct. You know nothing about the side lengths.

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  3. Amanda is constructing equilateral triangle JKL inscribed in circle M. To construct the inscribed polygon, she is going to use a compass to partition the circle into congruent arcs. To what width should she set the compass when partitioning the circle?

    A.
    The width must be equal to the radius of circle M.
    B.
    The width must be equal the diameter of circle M.
    C.
    The width can be equal to either the radius or the diameter of circle M.
    D.
    The width can be any size greater than the radius but less than the diameter of circle M.
    E.
    The width must be less than the radius of circle M.

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