Download 10-11reviewsheetanswerswebsite

Coordinate Geometry Proofs: Answer Key
1.
2. diagonals bisect, opposite sides congruent, opposite sides parallel, consecutive angles supplementary,
opposite angles congruent.
3. all of the properties of a parallelogram, consecutive sides congruent, diagonals perpendicular,
diagonals bisect angles.
4. all of the properties of a parallelogram, all right angles, diagonals congruent
5. all of the properties of a parallelogram, rectangle, and rhombus
6. only one set of parallel sides
7. all of the properties of a trapezoid, diagonals congruent, opposite angles supplementary, base angles
congruent.
8. TR = 4, TQ = 4, PR = 8, QS = 8
9. <B = 77
10. b = 2, AC = 10, BD = 10
11. side of a rhombus = 7
12. x = 10, <ADC = 60, <BAD = 60, <BCD = 120, <ABC = 120
***for all coordinate geometry proofs, you must write all of the formulas that you use and
show all work***
13. 1) prove parallelogram: diagonals bisect (MK & IE)
MK = (1.5, -.5)
IE = (1.5, -.5)
MK and IE bisect because they have the same midpoint
MIKE is a parallelogram because the diagonals bisect
2) prove rectangle: diagonals are congruent (MK & IE)
MK =
MK
IE =
IE because they have the same distance
MIKE is a rectangle because it’s a parallelogram whose diagonals are congruent
14. 1) prove parallelogram: diagonals bisect (AC & BD)
AC = (-.5, 4.5)
BD = (-.5, 4.5)
AC and BD bisect because they have the same midpoint
ABCD is a parallelogram because the diagonals bisect
2) prove rhombus: diagonals are perpendicular (AC & BD)
AC: m = 1
BD: m = -1
MK ⊥ IE because they have negative reciprocal slopes
MIKE is a rectangle because it’s a parallelogram whose diagonals are perpendicular
15. SKIP
16. 1) prove trapezoid: only one set of parallel sides.
FD =
DN = undefined
NY =
FY =
FD||NY because they have the same slope. DN is not || to FY because they do not have the
same slope.
FDNY is a trapezoid because it has only one set of parallel sides.
2) prove isosceles trapezoid: non-parallel sides are congruent
DN: d = 5
DN
FY: d = 5
FY because they are the same length
FDNY is an isosceles trapezoid because it is a trapezoid whose non-parallel sides are
congruent.