![]() ![]() ![]() ![]() How Do You Prove the Converse of Pythagoras Theorem? The converse of Pythagoras theorem formula is c 2 = a 2 + b 2, where a, b, and c are the sides of the triangle. ![]() What is the Formula for Converse of Pythagoras Theorem? The coverse of the Pythagoras theorem states that, in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. In other words, we can say, in a right triangle, (Opposite) 2 + (Adjacent) 2 = (Hypotenuse) 2.įAQs on Converse of Pythagoras Theorem What is the Converse of Pythagoras Theorem? Here, AB is the base, AC is the altitude or the height, and BC is the hypotenuse. In the given triangle ABC, we have BC 2 = AB 2 + AC 2. The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. If the sum of the squares of two sides of a triangle is greater than the square of the hypotenuse, the triangle is an acute triangle. If the sum of the squares of two sides of a triangle is less than the square of the hypotenuse, the triangle is an obtuse triangle.ģ. If the sum of the squares of two sides of a triangle is considered equivalent to the square of the hypotenuse, the triangle is a right triangle.Ģ. Once the triangle is identified, constructing that triangle becomes simple. The main application of the converse of the Pythagorean theorem is that the measurements help in determining the type of triangle - right, acute, or obtuse. The converse is the complete reverse of the Pythagoras theorem. The converse of Pythagoras theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. If DFCB is a parallelogram, BD=CF, and BD||CF, as opposite sides of a parallelogram.Ĭontinuing to work backward from the way we proved the original theorem, we will now show the triangles ΔADE and ΔCFE are congruent, and from this show that CE=EA, and also that CF=AD, and as a result BD=AD.What is the Converse of Pythagoras Theorem? We now have a quadrilateral, DFCB, in which there is a pair of opposite sides (DF and BC) which are both parallel (given) and equal in length (we constructed DF that way), and as we have shown such a quadrilateral is a parallelogram. 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. In today's geometry lesson, we will prove the Converse Triangle Midsegment Theorem. ![]()
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