Download Properties of Plane Figures

SOL 5.13a Geometry
NOTEPAGE FOR STUDENT
Page 1
Properties of Plane Figures
There are a number of plane figures that we should be able to recognize, identify, and
describe. A plane figure is one that takes up space on a plane. A plane is an endless flat
surface that exists in two dimensions. Those two dimensions are usually height and width.
A triangle is a polygon with three sides. Triangles can be named according to the kinds
of angles they contain: right, acute, and obtuse.
A right triangle has one right angle. The square in the corner of the angle tells us that it is
a right angle; a right angle measures 90°.
90°
An obtuse triangle has one obtuse angle and two acute angles. The obtuse angle is the
angle that measures greater than 90°.
> 90°
An acute triangle has three acute angles. Although the other triangles also have acute
angles in them, the acute triangle is the only one with three acute angles.
< 90°
Triangles can also be named according to the measurements of their sides. A scalene
triangle has no equal, or congruent, sides. An isosceles triangle has at least two sides
that are congruent. An equilateral triangle has all three sides congruent.
Scalene triangle
Isosceles Triangle
Equilateral triangle
All triangles have two names – one name referring to the angles and the other to the sides.
For example, the scalene triangle is also an obtuse triangle.
Think! What are the other names for the isosceles and the equilateral triangle?
©2011
SOL 5.13a Geometry
NOTEPAGE FOR STUDENT
Page 2
Properties of Plane Figures
A polygon with four sides is called a quadrilateral. There are many different kinds of
quadrilaterals that are named for their different properties. Some of these properties
include the kinds of angles they have and the length of their sides.
A parallelogram is a quadrilateral with two sets of parallel sides. Parallel means that
the points of the line segments are always the same distance apart.
Properties of a
parallelogram include the following:

The opposite sides of a parallelogram are congruent.

The opposite angles of a parallelogram are congruent.
a
1

2
c
Sides c and d are parallel line segments.
d

4
3
b

Sides a and b are parallel line segments.
Angles 1 and 3 are the same size.
Angles 2 and 4 are the same size.
A diagonal divides the parallelogram into two congruent triangles. The line segment
that connects the two vertices is called a diagonal. That means if we draw a line
segment from one opposite corner or vertex to the other, the parallelogram will be
divided into two congruent triangles.
A
C

D
B
The diagonals of a parallelogram also bisect each other. Bisect means to cut a
geometric figure into two equal or congruent halves. A bisector can be a line
segment (has a start and stop), a line (goes on forever in both directions), or a plane
figure. For example, in the parallelogram above, AB bisects CD .
©2011
SOL 5.13a Geometry
NOTEPAGE FOR STUDENT
Page 3
Properties of Plane Figures
One kind of parallelogram is a rectangle.
A rectangle has four right angles.
In this
example, the small squares in the corners of the rectangle mean that the angles are right
angles. A rectangle has all the same properties of a parallelogram.
right angles
Another kind of parallelogram is a square. A square is a rectangle with four sides of equal
length. Because a square is also a rectangle, it also has all the properties of a
rectangle and a parallelogram.
Another kind of parallelogram is a rhombus. Like a square, it has four congruent sides.
Unlike a square, a rhombus does not have right angles. A rhombus looks like a square that
leans. The opposite angles of a rhombus are congruent. Because a rhombus is a
parallelogram, it has all the properties of a parallelogram.
©2011
SOL 5.13a Geometry
NOTEPAGE FOR STUDENT
Page 4
Properties of Plane Figures
A trapezoid is a quadrilateral with only one pair of parallel sides. The parallel sides are
called bases, and the non-parallel sides are called legs.
If the legs are the same length, the trapezoid is called an isosceles trapezoid.
isosceles trapezoid
Not an isosceles trapezoid
base
leg
base
leg
leg
leg
base
base
PRACTICE!
1. Classify the properties of these quadrilaterals in a table to help remember them.
Name of figure
Sides of equal
length
Parallel sides
parallelogram
rectangle
square
rhombus
trapezoid
©2011
Right angles
Opposite
angles equal