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Magazine Problem 1
WRITING A quadrilateral has four congruent sides. Is the quadrilateral a parallelogram? Justify your answer.
Problem 1
VOCABULARYWhy do vertices connected by a diagonal of a polygon have to be nonconsecutive?
Problem 1
Describe the differences between a trapezoid and a kite.
Problem 1
VOCABULARY Why is a parallelogram always a quadrilateral, but a quadrilateral is only sometimes a parallelogram?
Problem 2
WRITING What should you look for in a parallelogram to know if the parallelogram is also a rhombus?
Problem 2
DIFFERENT WORDS, SAME QUESTION Which is different? Find 鈥渂oth鈥� answers. Construct a quadrilateral with opposite sides congruent. Construct a quadrilateral with one pair of parallel sides. Construct a quadrilateral with opposite angles congruent. Construct a quadrilateral with one pair of opposite sides congruent and parallel.
Problem 3
Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is isosceles. \(\mathrm{W}(1,4), \mathrm{X}(1,8), \mathrm{Y}(-3,9), \mathrm{Z}(-3,3)\)
Problem 3
In Exercises \(3-6,\) ind the sum of the measures of the interior angles of the indicated convex polygon. (See Example 1.) nonagon
Problem 4
Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is isosceles. \(\mathrm{D}(-3,3), \mathrm{E}(-1,1), \mathrm{F}(1,-4), \mathrm{G}(-3,0)\)
Problem 4
In Exercises \(3-8,\) for any rhombus \(JKLM,\) decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. $$ \angle \mathrm{K} \cong \angle \mathrm{M} $$
