Now, since DE=EF, and DE is half of BC, DF should be equal to BC. We proved the original theorem here - Triangle Midsegment Theorem, and did so by constructing another triangle by extending DE to point F so that DE=EF. Since this is a converse theorem, it is often a good strategy to solve the geometry problem by looking at how we proved the original theorem and do things in the opposite order. In other words: Show that BD=DA and CE=EA. In triangle ΔABC, DE is parallel to BC, and its length is equal to half the length of BC. We also prove another converse theorem - that if a line connecting two sides of a triangle is parallel to the third side and intersects one side’s midpoint, it is a midsegment. This is just one of several converse theorems for the triangle midsegment theorem. We will now prove the converse of this theorem - that if a line connecting two sides of a triangle is parallel to the third side and equal to half that side, it is a midsegment. The Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to the third side, and its length is equal to half the length of the third side. It cannot distinguish right triangles from non-right triangles.In today's geometry lesson, we will prove the Converse Triangle Midsegment Theorem. This theorem only applies to right triangles.
The converse theorem is used to determine if a triangle is correct.Converse of Pythagoras theorem can be used to find the length of one right triangle side if two sides are known.Therefore, the triangle is a right triangle.Įxample 2: Triangle GHI has sides of length 9, 40, and 41.Įxample of Converse of Pythagoras theorem To show that it is a right triangle, we use the converse of the Pythagorean theorem.
#Converse geometry triangles how to#
Here are 2 examples of how to use the converse of the Pythagorean theorem:Įxample 1: Triangle ABC has sides of length 5, 12, and 13. The Converse of Pythagoras theorem can be used in multiple fields, such as:Ĭonverse Of Pythagoras Theorem Solved Questions a 2 + b 2 = c 2, where a and b are the shorter sides and c is the hypotenuse.Ĭonverse of Pythagoras Theorem Applications.In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.The Converse of Pythagoras' theorem states that a triangle is valid if a 2 + b 2 = c 2. Pythagoras Theorem Detailed Video Explanation: So, the theorem states that a triangle is a right triangle if it has sides a, b, and c such that a 2 + b 2 = c 2.The assumption must be false, and the triangle must be a right triangle. Therefore, a 2 + b 2 = c 2, it can be claimed that the triangle is not a right triangle and is refuted.According to the Pythagorean theorem, the sum of the squares of the shorter sides (a 2 + b 2) will be less than the square of the longest side (c 2). Initially, it can be supposed that the triangle is not a right triangle. The converse of the Pythagorean theorem can be shown using the following logic: Given a triangle with sides a, b, and c, where c is the longest side, and a 2 + b 2 = c 2, it must be proved that the triangle is a right triangle.
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