![]() We have already proven that for the general case of parallel lines, a transversal line creates interior angles that sum up to 180 °. Therefore, its a simple use of the properties of parallel lines to show that the consecutive angles are supplementary. Show that i) it bisects ∠C also, ii) ABCD is a rhombus. The definition of a parallelogram is that both pairs of opposing sides are parallel. ![]() Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure).Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.Show that the diagonals of a square are equal and bisect each other at right angles.Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. You can prove that a quadrilateral is a parallelogram by showing that both pairs of opposite sides are parallel and equal in length. Given: ABCD is a parallelogram and line segments AX, CY bisect the angles A and C respectively. Theorems on Parallelograms: If we put the sharp tip of a pencil on a sheet of paper and move from one point to the other without lifting the pencil, then the shapes so formed are called plane curves.A curve that does not cross itself at any point is called a simple curve.If the diagonals of a parallelogram are equal, we have proved that it is a rectangle. NCERT Maths Solutions Class 9 Chapter 8 Exercise 8.1 Question 2 From the equations we can see that the slopes of the lines. Is this quadrilateral a parallelogram To check if its a parallelogram we have to check that it has two pairs of parallel sides. A quadrilateral is defined by the four lines (y2x+1), (yx+5), (y2x4), and (yx5). In most systems of axioms, the three criteriaSAS, SSS and ASAare established as theorems. Determining if a Quadrilateral is a Parallelogram. The ASA Postulate was contributed by Thales of Miletus (Greek). Video Solution: If the diagonals of a parallelogram are equal, then show that it is a rectangle ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. ☛ Check: NCERT Solutions for Class 9 Maths Chapter 8 Since ABCD is a parallelogram and one of its interior angles is 90°, ABCD is a rectangle. It is known that the sum of the measures of angles on the same side of transversal is 180° (co - interior angles) To show that ABCD is a rectangle, we have to prove that one of its interior angles is 90°.ĪB = DC (Opposite sides of a parallelogram are equal) To show that a given parallelogram is a rectangle, we have to prove that one of its interior angles is 90° and this can be done by the concept of congruent triangles. Given: The diagonals of a parallelogram are equal. Let’s look at ALE and CLB: ALE CLB (vertically opposite angles). ![]() If the diagonals of a parallelogram are equal, then show that it is a rectangle
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