# How to prove the triangle exterior angle theorem

Exterior Angle Theorem – Explanation & Examples

The exterior angle theorem states that if a triangle’s side gets an extension, then the resultant exterior angle would be equal to the sum of the two opposite interior angles of the triangle. According to the Exterior Angle Theorem, the sum of measures of ?ABC and ?CAB would be equal to the exterior angle ?ACD. How to prove the Exterior Angle Theorem; Exterior Angle Theorem. An exterior angle of a triangle is formed by any side of a triangle and the extension of its adjacent side. The Exterior Angle Theorem states that. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The following diagram shows the exterior angle theorem.

The exterior angle of a triangle is the angle formed between one side and the extension of its adjacent side. States the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite or non-adjacent interior angles.

Here, we will apply the exterior angle theorem to find the missing interior or exterior angles in a triangle. Your email address will not be published. Save my name, email, and website in this browser for the next time I comment.

All rights reserved. Reproduction in whole or in part without permission is prohibited. Table of Contents. Last modified on April 22nd, What is the Exterior Angle of a Triangle The exterior angle of a triangle is the angle formed between one side and the extension of its adjacent side. How to Find Exterior Angles of a Triangle Here, we will apply the exterior angle theorem to find the missing interior or exterior angles in a triangle.

Triangle Exterior Angle Theorem

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. m ? 4 = m ? 1 + m ? 2 Proof: Given: ? P Q R To Prove: m ? 4 = m ? 1 + m ? 2. For a triangle: The exterior angle d equals the angles a plus b. The exterior angle d is greater than angle a, or angle b. An exterior angle of a triangle is equal to the sum of the two opposite interior angles, thus an exterior angle is greater than any of its two opposite interior angles; for example, in ?ABC, ?5 = ?a + ?b. The sum of an exterior angle and its adjacent interior angle .

Let us explore the exterior angle theorem as we scroll down. Also, there is a simulator for you to explore the exterior angle theorem, and try your hand at solving the interactive questions at the end. An exterior angle of a triangle is formed when any side of a triangle is extended.

Exterior Angle Theorem :. The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The remote interior angles are also termed as opposite interior angles. The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles.

This condition is satisfied by all the six external angles of a triangle. To use the exterior angle theorem in a triangle we first need to identify the exterior angle and then the associated two remote interior angles of the triangle. A common mistake of considering the adjacent interior angle should be avoided.

The theorem can then be used to find the measure of an unknown angle. Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles. Exterior angle theorem could be used to determine the measures of the unknown interior and exterior angles of a triangle. Let us see a couple of examples to understand the use of the exterior angle theorem.

Can you help her with the same? Martha is struggling to find the measures of all the interior angles of the given triangle. Can you help her? The third internal angle of the triangle can be given as.

Ryan is studying the applications of the exterior angle theorem. Consider the following figure. Here are a few activities for you to practice. The mini-lesson targeted the fascinating concept of exterior angle theorem. The math journey around exterior angle theorem starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds.

Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath. At Cuemath , our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. The remote interior angles are also called opposite interior angles. The remote interior angles are also termed opposite interior angles.

Exterior Angle Theorem. Go back to 'Triangles'. Book a Free Class. Some common facts about the triangle that are already known to us- A triangle has 3 internal angles which always add to degrees. It is a polygon with the least number of sides three sides. It has 6 external angles. Lesson Plan 1. What Is the Exterior Angle Theorem? Important Notes on Exterior Angle Theorem 3. Challenging Question on Exterior Angle Theorem 4. Solved Examples on Exterior Angle Theorem 5.

Interactive Questions on Exterior Angle Theorem. Important Notes. Challenging Question. Solved Examples. More Important Topics. Related Sections. What is Congruence? Midsegment of a Triangle. Acute Triangle. Law of Cosine. Pythagoras Theorem. Hypotenuse Leg Theorem. Corresponding sides. Triangle Inequality Theorem. Angle Sum Theorem. Obtuse Triangle. Median of a Triangle. Altitude of a Triangle.

Triangle Calculation: Find C. Congruent Triangles. Perpendicular Bisectors. Angle side angle. Isosceles Triangles.

Relative Magnitudes of Sides and Angles. The Triangle Inequality. Distance of a Point From a Line. Angle Bisector. Triangles - Same Base, Same Parallels. Triangle Areas - Basic Calculations. Basic Triangle Constructions. Advanced Triangle Constructions. Angle Sum Property. Proof of the Angle Sum Property. What is Similarity? Similarity in Triangles. Basic Proportionality Theorem.

Internal Division. Angle Bisector Theorem. AA Criterion in Triangles. SSS Criterion in Triangles. SAS Criterion in Triangles. Areas of Similar Triangles. Right Angled Triangle. Types of Triangles. Obtuse Triangles. Example 1. Example 2. Example 3.

## How to prove the triangle exterior angle theorem: 3 comments

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