Review 6.3 - 6.5
Geometry
Name: _____________________
Fill in the Venn Diagram with the correct letters.
A. squares
B. parallelograms
C. rhombuses
D. rectangles
H
B
D
A
E. isos. trapezoid
F. kite
G. trapezoid
H. quadrilaterals
C
G
F
E
Properties of Parallelograms:
both prs opp. sides ll
1. ___________________
both prs opp. sides =
2. ___________________
both prs opp. angles =
3. ___________________
consecutive angles supplementary
4. ___________________
diagonals bis. each other
5. ___________________
Additional Properties of Rectangles:
4 right angles
1. ____________________
diagonals =
2. ____________________
Additional Properties of Rhombi:
4 = sides
1. ____________________
diagonals
2. ____________________
diagonals bis. opp. angles
3. ____________________
Properties of Squares:
1.
2.
3.
4.
5.
4 right angles
____________________
diagonals =
____________________
4 = sides
____________________
diagonals
____________________
diagonals bis. opp. angles
____________________
o
45
o
45
45o o
45
45o
45o
45o
45o
Ways to prove a quadrilateral is a Parallelogram:
If both prs. opp. sides ll
1. _________________________________
=
2. _________________________________
If both prs. opp. sides
If both prs. opp. angles =
3. _________________________________
If the diags. bisect each other
4. _________________________________
If one angle is supplementary to both its consecutive angles
5. _________________________________
=
6. _________________________________
If one pr. opp. sides is both ll and
Ways to prove a quadrilateral is a Rectangle:
If quad. and 4 right angles
1. ______________________________
If
and 1 right angle
2. ______________________________
If
and diags. congruent
3. ______________________________
Ways to prove a quadrilateral is a Rhombus:
If quad. and 4 congruent sides
1. ______________________________
If
and one pr. consecutive sides congruent
2. ______________________________
diagonals perpendicular
If
and
3. ______________________________
If
and diagonals bisect opp. angles.
4. ______________________________
Ways to prove a quadrilateral is a Square:
If quad has 4 right angles and 4 congruent sides
1. __________________________________
If quad. is both a rectangle and a rhombus
2. __________________________________
Determine the most specific name for the quadrilateral with
vertices A(0,2), B(2,6), C(6,4) and D(4,0). Show and justify all
work.
Slopes:
BC: m = -1/2
Slopes are same so BC ll AD
AD: m = -1/2
B
Slopes are opp. recipr. so AD
C
AB
AB: m = 2
A
CD: m = 2
Slopes are same so AB ll CD
D
Since 2 prs opp. sides ll, ABCD is a parallelogram.
Since parallelogram with one right angle, ABCD is a
rectangle.
Lengths:
BC = 22 + 42 =
20 = 2
5
CD = 22 + 42 =
20 = 2
5
Since same
length, BC = CD
Since parallelogram with one pr. cons. sides congruent,
ABCD is a rhombus.
Since both rectangle and rhombus, ABCD is a square.
Determine the most specific name for the quadrilateral.
rectangle
rhombus
rectangle
1. ________ 2. ________
3. _______
parallelogram
4. ________
rhombus
parallelogram
square
5. ________
6. ________
7. _______
rhombus
8. ________