Ch 8 provides rigorous proofs of parallelogram properties and introduces the mid-point theorem. Students also learn conditions that make a quadrilateral a parallelogram.
The sum of angles of a quadrilateral is 360°. A parallelogram has: opposite sides equal and parallel, opposite angles equal, consecutive angles supplementary, and diagonals that bisect each other.
A quadrilateral is a parallelogram if: (1) both pairs of opposite sides are equal, or (2) both pairs of opposite angles are equal, or (3) diagonals bisect each other, or (4) one pair of opposite sides is both equal and parallel.
The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it. Converse: a line through the mid-point of one side, parallel to another side, bisects the third side.
Download: https://ncert.nic.in/textbook/pdf/iemh108.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
The line segment connecting the mid-points of any two sides of a triangle is parallel to the third side and is half its length. This powerful theorem is often used in coordinate geometry and construction proofs.
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