Properties of Plane Figures - Weebly
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°.
An obtuse triangle has one obtuse angle and two acute angles. The obtuse angle is the angle that measures greater than 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.
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?
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
c d
b
• 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.
• 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, [pic]bisects [pic].
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.
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.
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
leg leg leg leg
PRACTICE!
1. Classify the properties of these quadrilaterals in a table to help remember them.
|Name of figure |Sides of equal length |Parallel sides |Right angles |Opposite angles equal |
|parallelogram | | | | |
|rectangle | | | | |
|square | | | | |
|rhombus | | | | |
|trapezoid | | | | |
-----------------------
• Sides a and b are parallel line segments. Sides c and d are parallel line segments.
• Angles 1 and 3 are the same size. Angles 2 and 4 are the same size.
•
2
1
4
3
D
A
B
C
base
base
base
base
90°
> 90°
< 90°
[pic]
right angles
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