GRADE 9: QUARTER 1

MEASUREMENT AND GEOMETRY

CONTENT STANDARDS:

1. simple geometric concepts and notations.

2. perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal.

ANGLES

Basic Concepts and Figures

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.”

pARTS OF AN ANGLE

VERTEX

A vertex is a corner of an angle, a point where two lines/sides meet. O is the vertex in the given figure.

ARM

The two rays which join at a common point to form the angle are called the arms of the angle. Observe the figure given above which shows that OA and OB are the arms of the angle AOB.

INITIAL SIDE

Also known as the reference line, a straight line from where an angle is drawn. OB is the reference line.

TERMINAL SIDE

The side up to which the angle measurement is done. In the given diagram above, OA is the terminal side.

types of angles and their properties

There are six types of angles. Each type of angle has a unique identification on the basis of angle measurement. Let us read about each type of angle individually along with their properties.

1. Acute Angle

Definition: An angle less than 90°.
Range: 0° < angle < 90°
Property: It is always smaller than a right angle.

2. Right Angle

Definition: An angle exactly equal to 90°.
Property: Forms a perfect L-shape; indicates perpendicular lines.

3. Obtuse Angle

Definition: An angle greater than 90° but less than 180°.
Range: 90° < angle < 180°
Property: Wider than a right angle.

4. Straight Angle

Definition: An angle exactly equal to 180°.
Property: Looks like a straight line.

5. Reflex Angle

Definition: An angle greater than 180° but less than 360°.
Range: 180° < angle < 360°
Property: More than a straight line but less than a full rotation.

6. Full Rotation (Complete Angle)

Definition: An angle equal to 360°.
Property: Represents a complete turn or circle.

interior and exterior angles

Interior angles: Interior Angles are the angles formed within or inside a shape.

Exterior angles: Exterior angles are the angles formed outside a shape, between any side of a shape and an extended adjacent side.

complementary and supplementary angles

Apart from the aforementioned types, there are two more angle types which are complementary angles and supplementary angles. If the sum of two angles is equal to 180°, then they are supplementary angles, and if the sum is equal to 90°, then they are called complementary angles.

For a visual explanation and additional information, you might find this video helpful:

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