LINES AND ANGLE

Parallel Lines and a Transversal

Parallel lines with transversal

Parallel lines with a transversal

• $\angle 1=\angle 5,\angle 2=\angle 6,\angle 4=\angle 8and\angle 3=\angle 7$(Corresponding angles)
• $\angle 3=\angle 5,\angle 4=\angle 6$ (Alternate interior angles)
• $\angle 1=\angle 7,\angle 2=\angle 8$ (Alternate exterior angles)

Lines parallel to the same line

- Lines that are parallel to the same line are also parallel to each other.

Introduction to Geometry

Angles and types of angles

When 2 rays originate from the same point at different directions, they form an angle.

-    The rays are called arms and the common point is called vertex
-    Types of angles : (i) Acute angle $0^{\circ }<a<{90}^{\circ }$
                                 (ii) Right angle $a={90}^{\circ }$
                                 (iii) Obtuse angle : ${90}^{\circ }<a<{180}^{\circ }$
                                 (iv) Straight angle $={180}^{\circ }$
                                 (v) Reflex Angle ${180}^{\circ }<a<{360}^{\circ }$
                                 (vi) Angles that add up to ${90}^{\circ }$ are complementary angles
                                 (vii) Angles that add up to ${180}^{\circ }$ are called supplementary angles.

Intersecting Lines and Associated Angles

Intersecting and Non-Intersecting lines

• When 2 lines meet at a point they are called intersecting
• When 2 lines never meet at a point, they are called non-intersecting or parallel lines

Adjacent angles

2 angles are adjacent if they have the same vertex and one common point.

Adjacent angles

Linear Pair

When 2 adjacent angles are supplementary, i.e they form a straight line (add up to ${180}^{\circ }$), they are called a linear pair.

Vertically opposite angles

When two lines intersect at a point, they form equal angles that are vertically opposite to each other.

Basic Properties of a Triangle

Triangle and sum of its internal angles

Sum of all angles of a triangle add up to ${180}^{\circ }$

Exterior angle of a triangle = sum of opposite internal angles

- If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

$\angle 4$ is the exterior angle

- $\angle 4=\angle 1+\angle 2$