Introduction
Importance of triangles:
Triangles are important for several reasons:
Basic Shape in Geometry: Triangles are one of the simplest shapes in geometry. Learning about triangles helps students understand more complex shapes and geometric concepts.
Properties and Measurements: Studying triangles teaches about angles, sides, and how to measure them. This is crucial for understanding geometry and solving problems.
Stability in Structures: Triangles are used in construction because they are very stable. They don't change shape easily, which makes buildings and bridges stronger.
Problem Solving Skills: Working with triangles can improve problem-solving and logical thinking skills, which are valuable in many areas of life and study. It's time to study the basic properties of a triangle. Like other polygons, triangles have their own classification and properties which is useful for understanding and creating the world around us.
A triangle is a fundamental geometric figure made by joining three
Here is ∆ABC. It has:
1. Sides: AB, BC , CA
2. Angles: ∠BAC, ∠ABC, ∠BCA
3. Vertices: A, B, C
The side opposite to the vertex A is
Can you name the angle opposite to the side AB?
We know how to classify triangles based on the (i) sides (ii) angles.
1. Based on Sides:
All sides and angles unequal:
Two sides equal:
All sides are equal:
2. Based on Angles:
Every angle in this triangle is less than 90 degrees:
Contains one angle greater than 90 degrees:
Features one angle that is exactly 90 degrees:
1. Write the six elements (i.e., the 3 sides and the 3 angles) of ∆ABC.
∆ABC
Solution:
The 3 sides of Triangle are:
The 3 angles of Triangle are:
∠A, ∠B, ∠C or ∠
2. Write the:
a
(i) Side opposite to the vertex Q of ∆PQR
Solution:
∆PQR
Side opposite to vertex Q of △PQR is
b
(ii) Angle opposite to the side LM of ∆LMN
Solution:
∆LMN
Angle opposite to the side LM is ∠N or ∠LNM or ∠
c
(iii) Vertex opposite to the side RT of ∆RST
Solution:
∆RST
Vertex opposite to the side RT of △RST is
3. Look at Fig and classify each of the triangles according to its
(a) Sides
(b) Angles
a
∆ABC
Solution:
(i) The triangle ABC
Based on Side: In Triangle ABC, since two sides (BC and AC ) are equal (= 8 cm ).
The given triangle is an
Based on Angle: In Triangle ABC, since all the triangles are less than
So the given triangle is Acute angled triangle.
b
∆PQR
Solution:
(ii) The Triangle PQR
Based on Side: In Triangle PQR, all the sides are different so, The given triangle is a
Based on Angle: In Triangle PQR, since angle QRP is a
So the given triangle is Right-angled triangle.
c
∆LMN
Solution:
(iii)The Triangle LMN
Based on Side: In Triangle LMN, since two sides (MN and NL ) are equal (=7 cm ), The given triangle is an
Based on Angle: In Triangle LMN, since angle MNL is an
So the given triangle is Obtuse angled triangle.
d
∆RST
Solution:
(iv) The Triangle RST
Based on Side: In Triangle RST, all the sides are equal (=5.2 cm) so, The given triangle is an
Based on Angle: In Triangle RST, since all the triangles are less than
So the given triangle is Acute angled triangle.
e
∆ABC
Solution:
(v)The triangle ABC
Based on Side: In Triangle ABC, Since two sides (AB and BC ) are equal (= 3 cm ) The given triangle is an
Based on Angle: In Triangle ABC, Since angle ABC is greater than
So the given triangle is Obtuse angled triangle.
f
∆PQR
Solution:
(vi)The Triangle PQR
Based on Side: In Triangle PQR, Since two sides (PQ and QR ) are equal (= 6 cm ) The given triangle is an
Based on Angle: In Triangle PQR, Since angle PQR is a
So the given triangle is Right-angled triangle.