geometry venn diagrams help

of a quadrilateral: Two sides of a quadrilateral, which have no common point, are called opposite sides. In the diagram, AB and DC is one pair of opposite sides. AD and BC is the other pair of opposite sid..

In developing the geometry of parallel lines, observe the three lines arrangement 'l', 'm' and 't'. In the diagram 'l' and 'm' are coplanar. They may be parallel as in figure 't' intersects 'l' and 'm' at two distinct points 'A' and 'B' and at 'C' and 'D'. Line t is called a tra..

Transversal - In developing the geometry of parallel lines, observe the three lines arrangement 'l', 'm' and 't'. In the diagram 'l' and 'm' are coplanar. They may be parallel as in figure 't' intersects 'l' and 'm' at two distinct points 'A' and 'B' and at 'C' and 'D'. Line t i..

In quadrilateral DBCF, DB||CF (by construction) DF||BC (given) DBCF is a parallelogram. DB=CF ----(i) (opposite sides of a parallelogram) But DB=AD ----(ii) (given) From (i) and (ii), AD=CF Now compare triangles, AED and CEF, AD = CF \ AE = EC (CPCT) That is E is the mid point of AC. Hen..

A pair of angles are said to be alternate angles if (i) both are interior angles (ii) they are on the opposite sides of the transversal and (iii) they are not adjacent angles. Alternate angles are some times also called alternate interior angles. In the diagram..

Consider the statement of a theorem "If a transversal intersects two parallel lines, then pairs of corresponding angles are equal”. This theorem has two parts. If (hypothesis) and then (conclusion). Let us interchange the hypothesis and conclusion and write the statement. "If a..

Parallelograms - Parallelogram is a quadrilateral whose opposite sides are parallel and equal. A rectangle, a rhombus and a square are considered as parallelograms. A trapezoid is quadrilateral with exactly one pair of opposite sides being parallel. Hence, it is not a parallelogram. You have learnt..

Introduction - Recall that if two straight lines are not parallel, they meet at a point when produced. Observe lines l and m which meet at a point (O). In the diagram, l and m are called intersecting lines. O is called the point of intersection. Similarly two line segments or two rays may..

In the diagram and are two coplanar lines. PQRS is a transversal intersecting at Q and at R. Eight angles are formed, they are numbered from 1 to 8. By virtue of their locations, some of the angles can be paired together. The paired angles are given special names (apart from ad..

Question: In the following diagrams parallel lines are marked by arrows in the same direction. Transversal is also drawn. Find the missing angles and provide the reason for each. Note: (No proof is required but the essential steps of working must be given) Answer: (i) Find a,..