Triangle Angle-Sum Theorem - Watch video (Geometry)

Geometry: Triangle Angle-Sum Theorem

This is a free lesson from our course in Geometry


	In this lesson you’ll explore the basics and approach toward logic about proving the important theorems, corollary related to of triangle angle-sum theorem and how to use the properties for applications. The related contents, explanation with examples are presented by instructor using video and in own hand writing. This will provide the geometry help; in context with triangles angle-sum and to apply the developed skills, for finding solution to real-world problems. Theorem- ‘the sum of the angles of any triangle is 180° i.e. two right angles’. Given: PQR is a triangle. Proof: E + F + G = 180 (More text below video...)

Other useful lessons:

Triangles Classification

Triangle Inequality

Medians and Midsegment

(Continued from above)

Corollary: a corollary is a statement that can be easily proved by applying a theorem. Corollary of the theorem is- ‘if one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles.

Exterior Angle of a Triangle
Given: Angle x is an exterior angle of the triangle:

You know that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices, i.e.

x =

a +

b in the above figure.

Proof:

In the triangle, three angles add up to 180

. Therefore; a + b + y = 180

.
The angles on a straight line QRS, add up to 180

. Therefore; x + y = 180

. Thus y = 180 - x. Substitute this value of y into the first equation, you’ll get: a + b + 180 - x = 180. On rearranging you get, a + b = x.
Hence proved.
This can also be written as,
Given:

PQR, in which QR is extended to S. Prove: PRS =

P +

Q. In the figure above, x measures 124

, find measure of angle a, y & b, if PQ=PR.
Proof:
Notice that, m

x = m

a + m

b. Since PQ and QR are equal in length, it is case of an isosceles triangle. Therefore, m

a = m

b. These are respectively 62

each and m

y equals to 56

.
Remember: in any triangle,
• the angles of a triangle sum up to 180

. Each angle in equilateral triangle equals to 60

.
• an angle opposite the greatest side is the greatest angle, and also inverse is true.
• angles opposite to the equal sides are equal. Especially all the angles in an equilateral triangle are equal.
• exterior angle of a triangle is equal to a sum of interior angles at other two vertices.
• any side of a triangle is less than a sum of two other sides, and more than their difference.
The video above will explain more details about Triangle Angle-Sum Theorem and relationship of the involved properties, with the help of several examples and practice problems.

Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.

-	All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic.
-	We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the problem-solving process!
-	Winpossible courses have been used by students for help with homework and by homeschoolers.
-	Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.