Angle Properties

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GEOMETRY:

GEOMETRY ANGLE PROPERTIES

Angles on a straight line:

1. Angles on a straight line add up to 180 degrees. Angles on a straight line

Angles in Parallel lines:

Angles in Parallel lines 1 . Alternate Angles : When two lines are parallel to each other and cut by a transversal then alternate angles are equal. Here B = a Alternate angles form a Z.

Parallel Lines:

Corresponding Angles : When two lines are parallel to each other, then corresponding angles are also equal. Parallel Lines

Parallel Lines:

Interior Angles are supplementary in parallel lines. Parallel Lines

Vertically Opposite Angles::

They are formed at the point of intersection of two lines and are always equal. Vertically Opposite Angles:

Angles of a Triangle.:

Angles of a Triangle. A Triangle has 3 sides and 3 angles . The sum of all interior angles of a triangle = 180 degrees. Exterior Angle = Sum of two interior opposite Angles.

Angles in Polygons::

Angles in Polygons: A Polygon consists of 1 or more triangles. We can find the sum of Interior Angles of a polygon by dividing it into various triangles. Sum of Interior Angles = ( n-2) x 180 Quadrilateral : No of sides = 4 Sum of Interior Angles = (4 – 2) x 180 = 360 ⁰ Pentagon : No of sides = 5 Sum of Interior Angles = (5 – 2) x 180 = 540 ⁰

Angles of a regular Polygon are equal.:

Angles of a regular Polygon are equal.

Exterior Angles of a Regular Polygon always add up to 360⁰:

Exterior Angles of a Regular Polygon always add up to 360⁰ The Exterior Angles of a regular hexagon is 360/6 = 60⁰ The Interior Angle and its corresponding exterior Angle add up to 180⁰ [ 120⁰ + 60⁰ = 180⁰ ] Q . Calculate the exterior angles of a regular Octagon

Find the value of x.:

Find the value of x.

Angles in a Circle:

Angles in a Circle We say “ If two angles stand on the same chord, then the angle at the centre is twice the angle at the circumference ”

It’s still true when we move The apex, A, around the circumference. :

It’s still true when we move The apex, A, around the circumference. Of course, the reflex angle at the centre is twice the angle at circumference too!!

Angles in a Circle:

Angles in a Circle ∠AOB = 180⁰ ∠AOB = 2∠APB ∠APB = ½∠AOB ∠APB = 90⁰

Segment of a Circle.:

Segment of a Circle.

Angles in the same and different segments.:

Angles in the same and different segments. Angles in different Segment. Here ∠APB and ∠AQB are in different segments. Angles in different segments are not equal but are Supplementary. Angles in the same segment are equal . ∠PRQ and ∠PSQ are in the same segments. . ∠PRQ = ∠PSQ

Prove that angles in same segment are equal.:

Prove that angles in same segment are equal.

Cyclic Quadrilateral:

Cyclic Quadrilateral ∠A +∠c = 180⁰ , ∠B +∠D = 180⁰

Tangents to a Circle:

Tangents to a Circle

Tangents to a Circle:

Tangents to a Circle

Tangents to a Circle:

Tangents to a Circle

Questions::

Questions:

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