Ch 6 proves theorems about lines and angles at the Class 9 level, moving from verification to formal proof. Students prove properties of parallel lines cut by transversals and the angle sum property of triangles.
Linear pair axiom: if a ray stands on a line, adjacent angles sum to 180°. Converse: if adjacent angles sum to 180°, the non-common arms form a line. Vertically opposite angles are always equal (proved using linear pair).
If two parallel lines are cut by a transversal: alternate interior angles are equal (and conversely), co-interior (same-side interior) angles are supplementary (and conversely), corresponding angles are equal (and conversely).
The sum of the three interior angles of any triangle is 180°. Proof uses the parallel line through a vertex. Corollary: an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Download: https://ncert.nic.in/textbook/pdf/iemh106.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
Co-interior angles (also called same-side interior or consecutive interior angles) are interior angles on the same side of the transversal. When lines are parallel, they sum to 180° (supplementary).
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