Geometry is the branch of mathematics that deals with shapes, sizes, and properties of figures. This chapter introduces the fundamental building blocks of geometry.
Point, Line, Line Segment, and Ray
A point marks an exact location. It has no length, breadth, or thickness. Points are named with capital letters: A, B, P.
A line is a straight path that extends in both directions without end. It has no endpoints.
A line segment is part of a line with two endpoints. It has a definite length.
A ray is part of a line with one endpoint, extending in one direction without end.
- Angle
- An angle is formed when two rays start from the same point (called the vertex). The two rays are the arms of the angle. Angles are measured in degrees (°).
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: between 90° and 180°
- Straight angle: exactly 180°
- Reflex angle: between 180° and 360°
- Curves and Polygons
- A curve is a drawing made without lifting the pencil. It can be open or closed.
- A polygon is a closed figure made of straight line segments. Polygons are named by the number of sides:
- Triangle: 3 sides
- Quadrilateral: 4 sides
- Pentagon: 5 sides
- Hexagon: 6 sides
- Circle
- A circle is a closed curve where all points are at the same distance from the centre. Key terms:
- Radius: line from centre to any point on the circle.
- Diameter: chord passing through the centre = 2 x radius.
- Chord: line segment joining two points on the circle.
- Arc: part of the circle between two points.
- Sector: region between two radii and an arc.
- Segment: region between a chord and an arc.
How many lines can be drawn through a single point?
Infinitely many lines can pass through one point.
How many lines can be drawn through two distinct points?
Exactly one line can pass through two distinct points.
Classify the angle of 135°.
135° is between 90° and 180°, so it is an obtuse angle.
Name all the triangles in a figure that shows triangle ABC with point D on BC.
Triangles: ABD, ADC, ABC (three triangles).
If the radius of a circle is 7 cm, what is its diameter?
Diameter = 2 x radius = 2 x 7 = 14 cm.
A polygon has 8 sides. What is it called?
A polygon with 8 sides is an octagon.
Is a circle a polygon? Explain.
No, a circle is not a polygon because polygons are made of straight line segments, and a circle is a curved figure.
- Key Formulas
- Diameter = 2 x Radius
- A triangle has 3 sides, 3 angles, 3 vertices.
Common mistakes
- A line segment has two endpoints; a ray has only one; a line has none.
- The diameter is the longest chord of a circle.
- Parallel lines never meet, even when extended.
Summary
Geometry starts with points, lines, and angles. Polygons are closed figures with straight sides. A circle is defined by its centre and radius. Understanding these basics is essential for all further geometry.