Download Algebra in Geometry WS 2

Algebra in Geometry quads WS
Geometry
Name ________________________
Date __________ Block _______
Review Properties First!
List all the quadrilaterals that have each of the following properties—Do
NOT abbreviate the names…
A. Quadrilaterals with diagonals that bisect each other.
B. Quadrilaterals with only one pair of parallel sides.
C. Quadrilaterals with all pairs of consecutive angles congruent.
D. Quadrilaterals with congruent diagonals.
E. Quadrilaterals whose diagonals bisect the angles.
F. Quadrilaterals with perpendicular diagonals.
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1. Two angles formed by one diagonal of a rectangle and the sides of
the rectangle are x 2 + 6 x + 50 and −10 x + 8 . Find the measures of the two
angles.
2. Two consecutive angles in a parallelogram are represented by
x 2 + 6 x + 50 and x 2 + 6 x + 50 . Find all possible measures for the angles.
3. Opposite sides in a parallelogram are represented by 12 x 2 − 10 x and
−2 x 2 + 13 x − 3 . If x is greater than one, find the lengths of the sides of the
parallelogram.
4. Two consecutive angles of a parallelogram are represented by
2x 2 + x + 50 and x 2 + 6 x + 100 . If x is an integer, find the measures of the
angles.
5. Opposite angles in a parallelogram are represented by 25 x 2 − 5 x + 4
and 15 x . Find the measures of all angles of the parallelogram.
6. Two angles formed by one diagonal of a rectangle and the sides of
the rectangle are x 2 + 2 x + 50 and 5 x + 50 . If the smaller angle is greater
than 30, find the measures of the two angles.
7. Two consecutive angles of a parallelogram are x 2 + 2 x + 150 and 3x + 6 .
Find the measures of the angles.
8. Opposite sides in a parallelogram are represented by x 2 − 45 and
2 x + 35 . Find the two possible lengths of the sides.
9. Two consecutive angles of a parallelogram are represented by
x 2 − 20 x + 100 and x 2 + 9 x + 59 . If x is a positive integer, find the measures of
the angles.
10. Opposite angles in a parallelogram are represented by 7 x 2 + 17 x − 21
and −3 x 2 − 12 x . To the nearest degree, find the measures of all of the
angles of the parallelogram.
11. Two angles formed by one diagonal of a rectangle and the sides of
the rectangle are 10 x 2 − 18 x + 80 and 11x 2 + 7 . Find the measures of the two
angles.