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...)
<h2> Triangle Angle-Sum Theorem </h2> <p> triangles, angle, video, geometry, triangle angle sum-theorem, measure, example, triangle sum theorem, angle theorem, geometry tutorials, geometry help, interior angles, practice questions, quizzes</p> <p> The angle-sum theorem states that the sum of the measures of the interior angles of a triangle is 180°.</p>
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.

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.
Notice that, mx = ma + mb. Since PQ and QR are equal in length, it is case of an isosceles triangle. Therefore, ma = mb. These are respectively 62each and my 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.
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