Theorem
Theorem is a statement that is accepted as true only after proving that it is a consequence of the axiom..
Theorem 1
Parallelograms on the same base and between the same parallels are equal in area. ABCD and ABEF are two parallelograms on the same base AB and between the same parallels AB, DE area (ABCD) = area (ABEF) An alternate way of proving this theorem is as follows: Since both parallelo..
Parallelograms on the same base and between the same parallels are equal in area. ABCD and ABEF are two parallelograms on the same base AB and between the same parallels AB, DE area (ABCD) = area (ABEF) An alternate way of proving this theorem is as follows: Since both parallelo..The Intercept Theorem
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. AP || BQ || CR. The intercepts AB and BC are equal. PQ, QR are the intercepts on any other line. PQ = QR Through A and B draw AE and BF parallel to PQR to cut B..
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. AP || BQ || CR. The intercepts AB and BC are equal. PQ, QR are the intercepts on any other line. PQ = QR Through A and B draw AE and BF parallel to PQR to cut B..Theorem 2
The area of a parallelogram is equal to that of a rectangle of the same base and of the same altitude. ABCD is a parallelogram and ABEF is a rectangle. They have common base AB and same height AF (or BE) Corollary Parallelograms having equal bases and equal altitudes are equal in area. A diagonal b..
The area of a parallelogram is equal to that of a rectangle of the same base and of the same altitude. ABCD is a parallelogram and ABEF is a rectangle. They have common base AB and same height AF (or BE) Corollary Parallelograms having equal bases and equal altitudes are equal in area. A diagonal b..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..
Theorems on concurrence
Through the activities suggested you will find that the angle bisectors, the perpendicular bisectors of sides, the altitudes and the medians of a triangle are concurrent. Now medians of a triangle are concurrent. Now we shall prove these properties by logical deductions. The point of con..
Midpoint Theorem
Introduction - We can prove some more properties of triangles using the properties of parallelograms seen in the previous chapter. We find that the line segment joining the mid points of any two sides of the triangle is parallel to the third side and is equal to half of it. We proveh..
Theorem 4
Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other. What is the additional property of the diagonals of a rectangle? Let us draw a rectangle and measure its diagonals. By measurement, you wil..
Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other. What is the additional property of the diagonals of a rectangle? Let us draw a rectangle and measure its diagonals. By measurement, you wil..Corollary of Theorem
If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles. In ABC, BC is produced to D. If in a triangle ABC, the bisectors of the angles ABC and ACB meet at M, prove..
If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles. In ABC, BC is produced to D. If in a triangle ABC, the bisectors of the angles ABC and ACB meet at M, prove..Theorem 2 (Converse of Theorem 1)
ABC is a triangle, the bisector of meets AB at X. A point Y lies on CX such that AX = AY. Prove that and AX = A..
ABC is a triangle, the bisector of meets AB at X. A point Y lies on CX such that AX = AY. Prove that and AX = A..See what our Users say :
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