Download Properties of Quadrilaterals

Geometry
HS Mathematics
Unit: 06 Lesson: 01
Properties of Quadrilaterals
Properties of convex quadrilaterals:
 Have four sides.
 Have four vertices and angles.
 Sum of the angles equals 360o.
 Are congruent if their corresponding angles and corresponding sides are congruent.
Quadrilaterals are generally classified by the number of parallel sides they contain. Study the
definitions below.
 Trapezium – a quadrilateral with no pairs of parallel sides
o Kite – two congruent pairs of adjacent sides
 Property Diagonals are perpendicular.
 One of the diagonals bisects the other.
 Trapezoid – a quadrilateral that has exactly one pair of parallel sides
o Isosceles trapezoid – non parallel legs are congruent
 Property The base angles of an isosceles trapezoid are congruent.
 Parallelogram – a quadrilateral with two pair of parallel sides, opposite sides are parallel
 Properties Opposite sides of a parallelogram are congruent.
 Opposite angles of a parallelogram are congruent.
 Consecutive angles of a parallelogram are supplementary.
 The diagonals of a parallelogram bisect each other.
o Rectangle – parallelogram with four right angles
 Property The diagonals of a rectangle are congruent.
o Rhombus – parallelogram with four congruent sides
 Property The diagonals of a rhombus are perpendicular to each other.
o Square – parallelogram with four right angles and four congruent sides
Practice Problems
1. Write a proof for the statement, “Consecutive angles of a parallelogram are supplementary.”
©2012, TESCCC
04/25/13
page 1 of 4
Geometry
HS Mathematics
Unit: 06 Lesson: 01
Properties of Quadrilaterals
2. Write a proof for the statement, “The diagonals of a rhombus are perpendicular.”
R
H
B
M
O
3. In the parallelogram below, BC = 2x – 7, AD = x + 5, and AC = 2x – 5. Find the value of x, BC,
AD, and AC.
B
C
A
D
4. In the rectangle below, LK = 3 and LM = 4. Find KN, MN, KM, LN, LJ, MJ, KJ, and NJ.
L
M
J
K
©2012, TESCCC
N
04/25/13
page 2 of 4
Geometry
HS Mathematics
Unit: 06 Lesson: 01
Properties of Quadrilaterals
5. How can a builder verify that each corner of a rectangular room forms a right angle
without measuring the angles?
6. A rug is being woven in the shape of a rhombus so that one diagonal is 6 ft. long and
the other is 8 ft. long. Fringe is to be place along the perimeter of the rhombus. How
much fringe will be needed to edge the rhombus?
7. Use the trapezoid below to determine the value of x, the value of y, mF, mG, and
mE.
F
G
(12x+60)º
(5y)º
(4x+40)º
80º
E
H
8. Use the trapezoid below to determine XW, YZ, mWXY, mWZY, and mXYZ.
X
Y
60º
W
©2012, TESCCC
Z
04/25/13
page 3 of 4
Geometry
HS Mathematics
Unit: 06 Lesson: 01
Properties of Quadrilaterals
9. What is the perimeter of the kite, if TV = 10 feet? Round answer to the nearest tenth.
U
45º
45º
V
T
60º
30º
W
©2012, TESCCC
04/25/13
page 4 of 4