ByRachit G Kulkarni

Class :- IX – BRoll Number :- 41

If we look around us, we will see angles everywhere.

•RAY: A part of a line, with one endpoint, that continues without end in one direction

•LINE: A straight path extending in both directions with no endpoints

•LINE SEGMENT: A part of a line that includes two points, called endpoints, and all the points between them

Intersecting Lines : Lines that cross

Non Intersecting lines : Lines that never cross and are always the same distance apart

• Hardwood Floor• Opposite sides of windows, desks, etc.• Parking slots in parking lot• Parallel Parking• Streets: Laramie & LeClaire

Two lines that intersect to form four right angles

•Window Panes•Streets Of Cities

Definition: A shape, formed by two lines or rays diverging from a common point (the vertex).

•Acute Angle•Right Angle•Obtuse Angle•Straight angle•Reflex Angle•Adjacent Angles•Linear Pair Of Angles•Vertically Opposite Angles

The measure of an angle with a measure between 0° and 90° or with less than 90° radians.

An angle formed by the perpendicular intersection of two straight lines; an angle of 90°.

Angle measures greater than 90 degrees but less than 180 degrees.

A straight angle changes the direction to point the opposite way. It looks like a straight line. It measures 180° (half a revolution, or two right angles)

A Reflex Angle is more than 180° but less than 360°

In geometry, adjacent angles, often shortened as adj. ∠s, are angles that have a common ray coming out of

the vertex going between two other rays. In other words, they are angles that are side by side, or

adjacent.

A pair of adjacent angles formed by intersecting lines. Linear pairs of angles are supplementary.

In geometry, a pair of angles is said to be vertical (also opposite and vertically opposite, which is abbreviated as vert. opp. ∠s ) if the angles are formed from two intersecting lines and the angles are not adjacent. They all share a vertex. Such angles are equal in measure and can be described as congruent.

Transversal :- A transversal, or a line that intersects two or more

coplanar lines, each at a different point, is a very useful line in

geometry.  Transversals tell us a great deal about angles. 

Parallel Lines :- Parallel lines remain the same distance apart over their entire length. No matter how far you extend them, they will never

meet.

•Corresponding Angles•Alternate Interior Angles•Alternate Exterior Angles•Interior Angles On The Same Side Of the transversal

The angles that occupy the same relative position at each intersection where a straight line crosses

two others. If the two lines are parallel, the corresponding angles are equal.

When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and inside the parallel lines, and the angles in each pair are congruent.

When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and outside the parallel lines, and the angles in each pair are congruent.

Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles. Further, many a times, we simply use the words alternate angles for alternate interior angles.

An exterior (or external) angle is the angle between one side of a triangle and the extension of an adjacent side.

1)Prove that exterioir angle of a triangle is equal to apposite interior angle2)Prove that vertically opposite angles are equal orProve that alternate Interior Angles Are equal4)In triangle poq∠ PQR =∠ PRQ . Then prove that ∠ PQS=∠ PRT.5) What value of x would make AOB a line if ∠AOC=4x ∠boc=6x+30 ° or7)If x + y = w + z, then prove that AOBis a line.

Thank you For Watching It & Your Co-orporation