How to Prove a Right Angle in Math

Updated February 21, 2017

A right angle is a 90 degree angle that forms where perpendicular 180 degree lines meet or cross. Proving that a polygon such as a square, rectangle or triangle has a right angle requires knowledge of shape properties, lines, sides, congruency, symbols and measurement tools. Proving right angles is a geometry technique that can help you solve problems where you have to find the measurement of other angles within a shape.

Find an angle that is labelled 90 degrees. Knowing that a right angle is worth 90 degrees is proof that you have identified a right angle. Look at a diagram of a shape to see if it has an angle with a small square drawn in it. The small square symbolises that an angle is worth 90 degrees, proving a right angle.

Study the types of lines so that you can identify perpendicular lines, which always meet or cross at a right angle. Prove that the angles of squares and rectangles are made by perpendicular lines and that perpendicular lines create right angles. Draw a small square in the angles of squares and rectangles to prove they have four right angles, each worth 90 degrees.

Learn the properties of quadrilaterals as having 360 degrees and that a geometry rule of squares and rectangles is that they have four equal angles. Divide 360 total degrees by four angles in rectangles and squares to prove that each angle is 90 degrees; hence a right angle.

Identify and prove a right angle in an isosceles right triangle by understanding that an isosceles triangle has two legs of the same measurements and a base of a different measurement. The two legs provide the same angle measurement. Find the measurement of one leg as 45 degrees, which means that congruent leg is 45 degrees. Add the leg measurements to get 90 degrees. Subtract 90 degrees from a total of 180 degrees, to prove that the base angle is a 90 degree right angle.

Identify and prove a scalene right angle by adding the two different angle measurements given and subtracting the total from 180 to find a right angle. Scalene triangles have three different angle measurements. Look at a straight leg and the base to see if they connect at a 90 degree angle.

Measure an angle with a protractor to prove that it is a right angle. Place the hole of the protractor, found on the straight edge of the tool, in the centre of the vertex of the right angle in question. Look at the numbers lining the curved edge of the protractor. Prove a right angle by showing that the angle lines up to the 90 degree marking on the protractor.

Things You'll Need

  • Protractor
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About the Author

Taylor DiVico is a professional songwriter, content writer, fiction novelist and poet with more than 15 years of experience. DiVico holds a B.A. in philosophy from the University of Rhode Island and an M.S. from Syracuse University.