Triangles and Polygons

Lesson Progress

0% Complete

Topic Content:

Proof: The sum of the angles of a triangle is 180º
Proof: The exterior angle of a triangle is equal to the sum of the opposite interior angles
Proof: The sum of the interior angles of any n-sided convex polygon is (2n-4) right angles
Summary of the Sum of Interior Angles of Various Polygons
Proof: The sum of the exterior angles of any convex polygon is 4 right angles

The study of Geometry brings out important theorems that serve as guiding principles in solving problems on triangles and polygons. Some of these theorems include:

1. The Sum of the Angles of a Triangle is 180º.

To prove: The sum of the angles of a triangle is 180º

The sum of the angles of a triangle is 180o — *_{Fig. 1.2.1}*

Given: any triangle XYZ

Required to prove: \( \scriptsize \hat{X} \: + \: \hat{Y} \: + \: \hat{Z} = 180º \)

Construction: extend \( \scriptsize \bar{YZ} \: to \: A \)

Draw \( \scriptsize \bar{ZB}\)parallel to \( \scriptsize \bar{YX}\)

Proof:

From Fig. 1.2.1 above:

x₁ = x₂ (alternate angles)

y₁ = y₂ (corresponding angles)

z + x₁ + y₁ = 180º (sum of angles on a straight line)

z + x₂ + y₂ = 180º (sum of angles in a triangle)

\( \scriptsize z = \hat{Z}, \: x_1 = \hat{X}, \: y_2 = \hat{Y} \)

∴ \( \scriptsize \hat{Z} \: + \: \hat{X} \: + \: \hat{Y} = 180º \)

\( \scriptsize \hat{X} \: + \: \hat{Y} \: + \: \hat{Z} = 180º \)

2. The Exterior Angle of a Triangle is

🔒 Premium Content

Full lesson notes for the term are available to subscribers only.

You are viewing an excerpt of this Topic. Subscribe Now to get Full Access to ALL this Subject’s Topics and Quizzes for this Term!

Click on the button “Subscribe Now” below for Full Access!

Subscribe Now

Note: If you have Already Subscribed and you are seeing this message, it means you are logged out. Please Log In using the Login Form Below to Carry on Studying!