Introduction
Geometry is the study of shapes and their properties. In this section, we focus on polygons like triangles and quadrilaterals, understanding their sides, vertices, and angles.
Explanation Step by Step
Geometric shapes are classified based on the number of sides and the measurement of their angles. A triangle has 3 sides, while a quadrilateral has 4 sides.
showing types of triangles and quadrilaterals based on sides and angles
Sub-topics
Triangles - Sides and Vertices
A triangle consists of 3 vertices, 3 sides, and 3 angles. The name of a triangle can be written in 6 different ways using its vertices.
Classification by Sides
- Equilateral Triangle: All three sides are equal.
- Isosceles Triangle: Two sides are equal.
- Scalene Triangle: All sides are of different lengths.
Classification by Angles
- Right-angled Triangle: One angle is 90 degrees.
- Acute-angled Triangle: All angles are less than 90 degrees.
- Obtuse-angled Triangle: One angle is greater than 90 degrees.
Examples
Example 1
Quadrilaterals and Types
A closed figure with four sides, four vertices, and four angles is called a quadrilateral.
- Square: 4 equal sides and 4 right angles.
- Rectangle: Opposite sides are equal and all angles are right angles.
- Rhombus: All 4 sides are equal.
- Kite: Pairs of adjacent sides are equal.
Tricks and Shortcuts
To identify a square: Check if all sides are equal AND all angles are 90 degrees.
Common Mistakes
Don't confuse a Rhombus with a Square; a Rhombus doesn't necessarily have 90-degree angles.
Practice Questions
Easy Questions
- How many vertices does a triangle have?
- What do you call a triangle with all sides equal?
- How many sides does a quadrilateral have?
Medium Questions
- Define an Obtuse-angled triangle.
- Is every rectangle a square? Explain why or why not.
- List the 6 ways to name Triangle XYZ.
Hard Questions
- If a quadrilateral has 4 equal sides but no right angles, what is it called?
- A triangle has sides 3 cm, 4 cm, and 5 cm. What type of triangle is it based on sides?
- Compare the properties of a Kite and a Rhombus.
Revision Summary
Triangles are 3-sided figures, and Quadrilaterals are 4-sided figures. They are categorized by the equality of their sides and the nature of their internal angles.
Some important reasons for this are as follows:
Right angled triangle: Q is a right angle (90°) in the figure
. Hypotenuse: The side opposite the right angle in a right triangle is called hypotenuse.
Here the side PR is the hypotenuse.
Property:The hypotenuse is the longest side in any right triangle.