What is an Angle Angles are formed by two rays or lines called the arms or sides of the angle, sharing a common endpoint, called the vertex of the angle. Types of angles There are various types of angles. The angles can be classified into two main types. Basis on their measure or magnitude. Based […]

Geometric Figure – Altitude Height – Definition In a geometric figure, the shortest distance between the base and its top, whether that top is an opposite vertex, an apex or another base.

How to draw a Circle of a Given Radius – Using Compass Circle A circle is a collection of all the points in a plane, whose all points are same distance from a fix point. The fix point is called center of the circle.  We use instruments for drawing a circle, on a paper whose […]

Parallelograms – Properties   A parallelogram is a special type of a polygon. it is a quadrilateral with both pair of opposite sides are parallel. Properties 1. Opposite sides are equal.       Opposite sides, AB = CD and AC = BD 2. Opposite angles are equal.      Opposite angles are ∠A = ∠D and ∠B […]

Given: Two triangles △ ABC and △ ABD are on same base (or equal bases) AB, and area of △ ABC and △ ABD are equal. Proof: CD ∥ AB Construction: Draw CE and DF perpendicular to AB.So DF is the height of △ ADB, and CE is the height of △ABC. CE perpendicular to AB and DF perpendicular to AB.Since, lines perpendicular to same line […]

Two triangles on the same base (or equal bases) and between the same parallels are equal in area. Given: △ ABC and △ PBC are two triangles on same base (or equal bases) BC and between the same parallels, BC and AP. To prove: ar △ ABC = ar △ PBC Construction: Through B, draw BD ∥ CA intersecting PA produced at D, and […]

The sum of the angles of a triangle is 180º Given: A triangle △ PQR and ∠1, ∠2, and ∠3 are angles of triangle △ PQR.  To prove:  ∠1 + ∠2 + ∠3 = 1800 Construction: Draw a line XPY parallel to QR passing through P.  Proof: XPY ∥ QR and PQ is transversal ∴ ∠2 = ∠4 (Alternate angles) ….(1) XPY ∥ QR and PR […]