Triangles Solved Examples
Example 1: In a triangle ∠ACD = 120°, and ∠ABC = 60°. Find the type of Triangle.
Solution:
In the above figure, we can say, ∠ACD = ∠ABC + ∠BAC (Exterior angle Property)
120° = 60° + ∠BAC
∠BAC = 60°
∠A + ∠B + ∠C = 180°
∠C OR ∠ACB = 60°
Since all the three angles are 60°, the triangle is an Equilateral Triangle.
Example 2: The triangles with sides of 5 cm, 5 cm, and 6 cm are given. Find the area and perimeter of the Triangle.
Solution:
Given, the sides of a triangle are 5 cm, 5 cm, and 6 cm
Perimeter of the triangle = (5 + 5 + 6) = 16 cm
Semi Perimeter = 16 / 2 = 8 cm
Area of Triangle = √s(s – a)(s – b)(s – c) (Using Heron’s Formula)
= √8(8 – 5)(8 – 5)(8 – 6)
= √144 = 12 cm2
Example 3: In the Right-angled triangle, ∠ACB = 60°, and the length of the base is given as 4cm. Find the area of the Triangle.
Solution:
Using trigonometric formula of tan60°,
tan60° = AB / BC = AB /4
AB = 4√3cm
Area of Triangle ABC = 1/2
= 1/2 × 4 × 4√3
= 8√3 cm2
Example 4: In ΔABC if ∠A+ ∠B = 55°. ∠B + ∠C = 150°, Find angle B separately.
Solution:
Angle Sum Property of a Triangle says ∠A+ ∠B+ ∠C= 180°
Given:
∠A+ ∠B = 55°
∠B+ ∠C = 150°Adding the above 2 equations,
∠A+ ∠B+ ∠B+ ∠C= 205°
180°+ ∠B= 205°∠B = 25°
Articles related to Triangles in Geometry:
Triangles in Geometry
Triangles in Geometry: A Triangle is a polygon with three sides and three corners. The corners are also known as vertices, and the sides that connect them are called edges. The interior of a triangle is a two-dimensional region. A triangle is the simplest form of a Polygon.
- Triangles can be classified based on their angles: Acute-angled, Obtuse-angled, and Right-angled.
- Triangles can be classified based on their sides: Equilateral, Isosceles, and Scalene.
Triangles are fundamental geometric shapes that play a crucial role in various fields, from mathematics and architecture to engineering and art. In this comprehensive guide, we delve into the world of triangles, uncovering their diverse properties, types, and real-world applications.
Let’s learn more about what are triangles in maths, their definition, types of triangles, formulas, examples, and practice problems in the article.
Table of Content
- Triangles Definition
- Triangle Shape
- Parts of a Triangle
- Angles in a Triangle
- Examples of Triangles in Geometry
- Properties of Triangles
- Types of Triangles
- Types of Triangles Based on Sides
- Equilateral Triangle
- Properties of Equilateral Triangle
- Equilateral Triangle Formulas
- Isosceles Triangle
- Properties of Isosceles Triangle
- Scalene Triangle
- Properties of Scalene Triangle
- Types of Triangles Based on Angles
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
- Angle Sum Property of a Triangle
- Triangle – Line of Symmetry
- Triangle Formulas
- Perimeter of Triangle
- Area of a Triangle
- Area of Triangle Using Heron’s Formula
- Steps to Find Area Using Herons Formula
- Congruent Triangles
- Ways to Prove Triangle Congruence:
- Properties of Congruent Triangles:
- Applications of Congruent Triangles:
- Similar Triangles
- Properties of Similar Triangles
- Formula of Similar Triangles
- Rules of Similar Triangles
- Applications of Similar Triangles
- Triangle Class 9
- Median of Triangle
- Altitude of Triangle
- Centroid of Triangle
- Circumcentre of a Triangle
- Orthocentre of a Triangle
- Incentre of a Triangle
- Fun Facts about Triangles
- Triangles Solved Examples
- Triangles in Geometry – Practice Problems
- Practice Questions on Triangles in Geometry