Pre-Test
Q&A	Triangles

Instruction 1-4

Definitions | Measuring Angles | Line and Angle Relationships | Triangles | Definitions of Figures | Summary

Now let's take a look at the various kinds of figures. This will be helpful when their properties and relationships are discussed in detail. Right now we will just concern ourselves with learning the definitions of these figures and identifying them. That way you can recognize them when we talk about their relationships and properties.

Before we get started, we need to make a definition: A closed figure is a figure that has an obvious interior and exterior. To travel to the interior from the exterior, you would have to cross a side.

Triangles
http://www.mathopenref.com/triangle.html
One frequently encountered figure in geometry is a triangle. A triangle is a closed figure formed by three segments. No two segments are on the same line (Figure 1.16). A triangle is denoted by sign followed by the labels of its vertices. For example the triangle in Figure 1.16 is denoted by ABC.

   
Figure 1.16

Each triangle has three interior angles and six exterior angles. An interior angle is formed by two sides of the triangle. CAB, CBA, and BAC are interior angles in ABC (Figure 1.17). An exterior angle is formed by a side and the extension of the side adjacent to it. For example, ABD and CAE are two exterior angles in ABC (Figure 1.17). The sum of the interior anglesof any triangle is 180˚.

http://www.mathopenref.com/triangleinternalangles.html
http://www.mathopenref.com/triangleextangle.html

Figure 1.17

Classification of Triangles
Basically, triangles are classified by the nature of their angles or their sides.

By Angles:

Right Triangle
http://mathworld.wolfram.com/RightTriangle.html
http://www.mathopenref.com/righttriangle.html 

If one of the interior angles in a triangle measures 90˚, it is called a right triangle (Figure 1.18). The sum of the other two angles in a right triangle is 90˚.

Figure 1.18

Obtuse Triangle.
http://www.mathwords.com/o/obtuse_triangle.htm
http://www.mathopenref.com/obtusetriangle.html

If the measure of one of the interior angles in a triangle is greater than 90˚, it is called an obtuse triangle (Figure 1.19).The measures of the other angles are always less than 90˚.

Figure 1.19

Acute Triangle
http://www.mathopenref.com/acutetriangle.html

If the measure of each interior angle in a triangle is less than 90˚, it is called an acute triangle (Figure 1.20).

Figure 1.20

Equiangular Triangle

If the interior angles of a triangle are congruent, it is called an equiangular triangle. The measure of each interior angle in an equiangular triangle is 60˚.

Figure 1.21
 

By Sides:
Scalene Triangle
http://mathworld.wolfram.com/ScaleneTriangle.html
http://www.mathopenref.com/scalene.html

In a scalene triangle, all the sides have different measures (Figure 1.22).

Figure 1.22

Isosceles Triangle
http://mathworld.wolfram.com/IsoscelesTriangle.html
http://www.mathopenref.com/isosceles.html

In an isosceles triangle, two or more sides are congruent. The congruent sides are called the legs of the triangle. The angle formed by the legs is called the vertex-angle and the side opposite the vertex-angle is called the base. For example, in isosceles triangle DEF (Figure 1.23), with , the legs are  and . As a result, D is the vertex-angle and makes the base. In an isosceles triangle, the angles at the ends of the base (the base angles) are congruent.

Figure 1.23

Equilateral Triangle
http://mathworld.wolfram.com/EquilateralTriangle.html
http://www.mathopenref.com/equilateral.html

In an equilateral triangle, all the sides are congruent (Figure 1.24). Also, all the interior angles are congruent. So we can consider an equilateral triangle the same as an equiangular triangle.

Any figure that is both equiangular and equilateral is called regular.

Figure 1.24
 

 for the entire dictionary. Click on Equilateral Triangle in the left pane, for example, for instruction and some quiz questions. For more instructional material on triangles go to:

www.factmonster.com/ipka/A0876325.html.

Please go to the links below for additional instruction for this topic included on the HSEE:

Study of Triangles:
http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=triang

Study of Quadrilaterals:
http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=quad

for Students, Parents and Teachers

Now let's do Practice Exercises 1-4 (top).

  Next Page:  Definitions of Figures (top)