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# Geometry Basics ŌĆō Recall

Draw two lines on a plane. They can be either parallel or intersecting.

Geometry Basics ŌĆōRecall

Draw two lines on a plane. They can be either parallel or intersecting.

Parallel lines        Two or more lines lying in the same plane that never meet.

Intersecting lines  Two lines which meet at a common point.

Perpendicular lines Two lines which intersect each other at right angle.

Concurrent lines  Three or more lines passing through the same point. ## 1. Types of Angles

Plumbers measure the angle between connecting pipes to make a good fitting. Wood workers adjust their saw blades to cut wood at the correct angle. Air Traffic Controllers (ATC) use angles to direct planes. Carom and billiards players must know their angles to plan their shots. An angle is formed by two rays that share a common end point provided that the two rays are non-collinear.  ### Complementary Angles

Two angles are Complementary if their sum is 90┬░. For example, if ŌłĀABC=64┬░ and ŌłĀDEF=26┬░, then angles ŌłĀABC and ŌłĀDEF are complementary to each other because ŌłĀABC + ŌłĀDEF = 90┬░ ### Supplementary Angles

Two angles are Supplementary if their sum is 180┬░.

For example if ŌłĀABC=110┬░ and ŌłĀXYZ=70┬░

Here ŌłĀABC + ŌłĀXYZ = 180┬░

Ōł┤ŌłĀABC and ŌłĀXYZ are supplementary to each other  Two angles are called adjacent angles if

i. They have a common vertex

ii. They have a common arm.

iii. The common arm lies between the two non-common arms.

### Linear Pair of Angles

If a ray stands on a straight line then the sum of two adjacent angle is 180┬░. We then say that the angles so formed is a linear pair. ŌłĀAOC + ŌłĀBOC=180┬░

Ōł┤ŌłĀAOC and ŌłĀBOC form a linear pair

ŌłĀXOZ + ŌłĀYOZ = 180┬░

ŌłĀXOZ and ŌłĀYOZ form a linear pair

### Vertically Opposite Angles

If two lines intersect each other, then vertically opposite angles are equal. In this figure ŌłĀPOQ = ŌłĀSOR

ŌłĀPOS = ŌłĀQOR

## 2. Transversal

A line which intersects two or more lines at a distinct points is called a transversal of those lines.

Case (i) When a transversal intersect two lines, we get eight angles.

In the figure the line l is the transversal for the lines m and n

(i) Corresponding Angles: ŌłĀ1 and ŌłĀ5, ŌłĀ2 and ŌłĀ6, ŌłĀ3 and ŌłĀ7, ŌłĀ4 and ŌłĀ8

(ii) Alternate Interior Angles:  ŌłĀ4 and ŌłĀ6, ŌłĀ3 and ŌłĀ5

(iii) Alternate Exterior Angles: ŌłĀ1 and ŌłĀ7, ŌłĀ2 and ŌłĀ8

(iv) ŌłĀ4 and ŌłĀ5,ŌłĀ3 and ŌłĀ6 are interior angles on the same side of the transversal.

(v) ŌłĀ1 and ŌłĀ8, ŌłĀ2 and ŌłĀ7 are exterior angles on the same side of the transversal. Case (ii) If a transversal intersects two parallel lines. The transversal forms different pairs of angles. ## 3. Triangles ## 4. Congruent Triangles

Two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of another triangle. Tags : Mathematics , 9th EM Mathematics : Geometry
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9th EM Mathematics : Geometry : Geometry Basics ŌĆō Recall | Mathematics