Converse of Pythagoras' Theorem
If the square on one side of a triangle is equal to the sum of the squares on the other two sides, the angle contained by these two sides is a right angle. In D ABC, if BC 2 = AB 2 + AC 2 then, A is a right ang..
If the square on one side of a triangle is equal to the sum of the squares on the other two sides, the angle contained by these two sides is a right angle. In D ABC, if BC 2 = AB 2 + AC 2 then, A is a right ang..Pythagoras' Theorem
In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle. ABC is a triangle with BAC = 90 o . BC 2 = AB 2 + AC 2 . On AB, BC and CA as sides, describe squares ABFG, BCDE and ACKL respectively. Draw AMN parallel to BE meeting..
In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle. ABC is a triangle with BAC = 90 o . BC 2 = AB 2 + AC 2 . On AB, BC and CA as sides, describe squares ABFG, BCDE and ACKL respectively. Draw AMN parallel to BE meeting..Converse
Any point (or every point) on the perpendicular bisector of the line segment joining two given points is equidistant from them..
Any point (or every point) on the perpendicular bisector of the line segment joining two given points is equidistant from them..Converse of a Theorem
Converse of a Theorem is the transposition of a statement consisting of 'data' and 'to prove' 'Data' becomes 'To Prove' and 'To prove' becomes 'Data' in the converse theorem..
Converse of a theorem
If two statements are such that the hypothesis of one is the conclusion of the other and vice-versa then either of the statement is said to be the converse of the other..
If two statements are such that the hypothesis of one is the conclusion of the other and vice-versa then either of the statement is said to be the converse of the other..Pythagoras Summary
Summary - In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle. In D ABC if A = 90 o , BC 2 = AB 2 + AC 2 . Conversely, if the square on one side of a triangle is equal to the sum of the squares on the other tw..
Summary - In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle. In D ABC if A = 90 o , BC 2 = AB 2 + AC 2 . Conversely, if the square on one side of a triangle is equal to the sum of the squares on the other tw..Theorem 2 (Converse of Theorem 1)
A Corollary is an easy consequence of a theorem. It two lines intersect, then the vertically opposite angles so formed are equal, and When a number of lines meet at a point, the sum of the angles so formed is four right angle..
A Corollary is an easy consequence of a theorem. It two lines intersect, then the vertically opposite angles so formed are equal, and When a number of lines meet at a point, the sum of the angles so formed is four right angle..Theorem2 (Converse of Theorem 1)
If two adjacent angles are supplementary, then their exterior arms lie in a straight lin..
Theorem 2 (Converse of Theorem 1)
If two angles of a triangle are equal, the sides opposite to these angles are equal. In AB = AC Draw AD, the bisector of to meet BC at D. ABC is a triangle, the bisector of meets AB at X. A point Y lies on CX such that AX = AY. Prove that ..
If two angles of a triangle are equal, the sides opposite to these angles are equal. In AB = AC Draw AD, the bisector of to meet BC at D. ABC is a triangle, the bisector of meets AB at X. A point Y lies on CX such that AX = AY. Prove that ..Converse of Theorem 4
Now consider the converse of this theorem..
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