Triangle types and properties | Class 7

      In this article we will study about Triangle.

•       what is Triangle and its types.
•        Triangle properties.
•        Median and Altitudes of Triangle .
•        Pythagoras Property.

Triangle Introduction

A triangle is a closed curve of three line segments. Triangle is denoted as Δ.

Types of Triangle

Types of Triangle is classified according to its sides and angles.

 

Based on sides there are three types of triangle .

 

• Equilateral
• Isosceles
• Scalene

 

Triangle types and properties | Class 7

Equilateral:-It is a triangle of three sides/line segments equal.

Isosceles:-An isosceles triangle is an triangle having a pair of sides equal .

Scalene:-A triangle having all three line segments unequal is known as scalene.

 

Based on angles there are three types of triangle .

 

• Acute
• Obtuse
• Right

 

Acute:-A triangle is said to be an acute triangle if it’s three angles measuring less than 90 degree.

 

Obtuse:-A triangle is said to be an obtuse triangle if it is having one obtuse angle (that is greater than 90degree).A triangle can only have one obtuse angle.

 

Right:-Right angled triangle is a triangle of having a right angle.

The side opposite to the right angle is hypotenuse.

 

Properties of triangle

• A triangle is comprised of 3 sides, 3 vertices, and 3 angles.
• The sum of three interior angles of a triangle is always 180degree.
• The sum of two sides (length) of a triangle is always greater than the length of the third side.
• The side opposite to the greater angle is the longest side of all the three sides of a triangle.
• The exterior angle of a triangle is always equal to the sum of its interior opposite angles. This property is called as an exterior angle property.

 

 

Medians of a triangle

    Median of a triangle is a line segment which joins the vertex of the triangle to the mid -point of its opposite side of the triangle.

Altitudes of a triangle

The altitude of a Triangle is a perpendicular line segment drawn from vertex to the side opposite to it. The side on which the perpendicular is being drawn is called its base.

Triangle types and properties | Class 7

Pythagoras property

In a right angled triangle square on the hypotenuse is equal to the sum of squares on the legs

 

Triangle types and properties | Class 7

Example- taken from class 7 exercise.

  Question 1- PQR is a right angled triangle at p.  If PQ = 10 cm and PR = 24cm.

   Find  QR ?

Answer-According to Pythagoras property

Triangle types and properties | Class 7

   QR²=PQ²+PR²

     QR²=10²+24²

       QR²=100+576

       QR²=676

     QR=26

Question 2-

       Is triangle the smallest polygon ?

 Answer- yes triangle is the smallest polygon. 

Question 3-

Circle Triangle Square and their definition.

Definition

Circle – The locus of points (plane two dimensional) located at the same distance from a given point is called a circle. This fixed point is called the center of the circle, the distance between the center and any point of the circumference of the circle is called the radius of the circle. The circle is a simple closed curve that divides the plane into two areas: an interior and an exterior. 

Triangle – A triangle is closed curve of line segments.

 Square –  Square is a type of quadrilateral with four equal sides and four right angles.

 

You must read topics on similarity and congruency of triangle.

 

Frequently Asked Questions

1 .What is triangle and its properties Class 7?

  Answer- Triangle-A triangle is a closed curve of three line segments.

   Properties of triangle-

·        A triangle is comprised of 3 sides, 3 vertices, and 3 angles.

·        The sum of three interior angles of a triangle is always 180degree.

·        The sum of two sides (length) of a triangle is always greater than the length of the third side.

·        The exterior angle of a triangle is always equal to the sum of its interior opposite angles. This property is called as an exterior angle property.

2. What do you mean by Triangle?

  Answer- Triangle –> tri + angle. Means three angles. A triangle is a closed curve of three line segments.

3. What is an isosceles triangle Class 7?

 Answer-A triangle in which two sides are of equal length is called an Isosceles Triangle.

4. How many types of triangles are there?

  Types of triangles are classified based on its sides and angles.

Based on sides there are three types of triangle .

 

• Equilateral
• Isosceles
• Scalene

Equilateral:-It is a triangle if three sides/line segments equal.

Isosceles:-A triangle having a pair of sides equal is known as isosceles.

Scalene:-A triangle having all three line segments unequal is known as scalene.

Based on angles there are three types of triangle.

• Acute
• Obtuse
• Right

 

Acute:-A triangle is said to be an acute triangle if it’s three angles measuring less than 90 degree.

Obtuse:-A triangle is said to be an obtuse triangle if it is having one obtuse angle (that is greater than 90degree).A triangle can only have one obtuse angle.

Right:-Right angled triangle is a triangle of having a right angle.

The side opposite to the right angle is hypotenuse.