Triangle, sides, interior angles, exterior angles, degrees and other properties

Triangles are one of the most fundamental geometric shapes and have a variety of properties characterizing their various parts: their interior angles (angles on the inside), their exterior angles, their sides as well as the relationship between each of these parts.

In the Triangle on the Left

Note: AB and BA are the same line. This holds true for any line segment: BC and CB are the same line, as well as AC and CA.

2) the angles are BAC, ACB and ABC

ABC is how we write "Triangle ABC" which is very different from ABC which means "angle ABC". (Be careful that you use the right mathematical symbol!)

Practice Problem One

Triangle's Parts

sides: JK,KL and LJ
angle 1: JKL or LKJ , angle 2 KJL or LJK, angle 3 JLK or KLJ

Identify the angles opposite the following sides:

Opposite Angles

JKKLJ
KLKJL
LJJKL

I. Total Number of degrees of interior angles in a triangle is exactly 180°.

To explore the truth of the statement above try Math Warehouse's interactive triangle, which allows you to drag around the different sides of a triangle and explore the relationship between the angles and sides. No matter how you position the three sides of the triangle, the total degrees of all interior angles (the three angles inside the triangle) is always 180°.
Practice Problems

Practice Problem One

What is the mLNM ? ( 'm' means 'measure' so this question is asking 'how many degrees is LNM ?")

LMN = 34°
MLN = 29°

Answer

Practice Problem Two

A triangle's angles are HOP, HPO and PHO.
mHOP is 64° and mHPO is 26°.
What is mPHO?

Measure of Angle

mPHO = 180°-26°-64°= 90°

II. The Relationship of Interior Angles and Sides
exterior angles

In any triangle, the largest interior angle is opposite the largest side; the smallest interior angle is opposite the smallest side and, not surprisingly, the middle-sized interior angle is opposite the middle-sized side.

To explore the truth of the statements you can use Math Warehouse's interactive triangle, which allows you to drag around the different sides of a triangle and explore the relationships betwen the measures of angles and sides. No matter how you position the three sides of the triangle, you will find that the statements in the paragraph above hold true.(All right, the isosceles and equilateral triangle are exceptions due to the fact that they don't have a single smallest side or, in the case of the equilateral triangle, even a largest side. Nonetheless, the principle stated above still holds true. !)

Practice Problem One

By looking at sizes of angles and sides of

STU, you should be able to tell which ones have the greatest size, least size or the middle size.

Answer

II. Relationship of Exterior And Interior Angles

An exterior angle of a triangle, or any polygon, is formed by extending one of the sides of the triangle (or polygon).

The exterior angle is supplemental to the adjoining interior angle. Notice: ABC =46° and the exterior angle is 134°.

Since 46+134=180, these angles are supplementary as is every exterior angle and its adjacent interior angle.

If the exterior angle,

1 = 110°what is m

2?

Answer

Triangles Side and Angles

Interior & Exterior Angles and sides