Basic Concepts in Geometry
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Theorem of remote interior angles of a triangle
- Congruence of Triangles
- Isoscles Triangle Theorem
- Property of 30-60-90 Triangle Theorem
- Median of a Triangle
- Perpendicular bisector Theorem
- Angle bisector theorem
- Properties of inequalities of sides and angles of a triangle
- Similar Triangles
Constructions of Triangles
Surface area and volume
- If pairs of opposite sides of a quadrilateral are congruent then that quadrilateral is a parallelogram.
- If both the pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram.
- If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
- A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
`square` ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove `square` APCQ is a parallelogram.
In the given figure, G is the point of concurrence of medians of Δ DEF. Take point H on ray DG such that D-G-H and DG = GH, then prove that `square` GEHF is a parallelogram.
Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.(shown in the given figure)
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square` PQRS is a parallelogram.