All questions of The Triangles and its properties for Class 7 Exam

Exterior angle is equal to opposite interior angle so, when we add 50 degree to 30 it will come 80 degree .. that 'A' is correct

(c) right- angled

Because it is an equilateral triangle

Equilateral Triangle: A Triangle with Equal Length Sides

An equilateral triangle is a specific type of triangle where all three sides are of equal lengths. It is a fundamental concept in geometry and is classified as a special case of triangles based on its side lengths.

Definition:
- An equilateral triangle is a polygon with three sides of equal lengths.
- Each internal angle of an equilateral triangle measures 60 degrees.

Key Points:
1. Equal Side Lengths: In an equilateral triangle, all three sides have the same length. This characteristic distinguishes it from other types of triangles.
2. Symmetry: Due to its equal side lengths, an equilateral triangle possesses symmetry. It can be folded along any of its medians, resulting in all three sides overlapping perfectly.
3. Regular Polygon: An equilateral triangle is the simplest form of a regular polygon. Regular polygons have all sides and angles equal.
4. Interior Angles: The interior angles of an equilateral triangle are all equal to 60 degrees. This means that when the angles are added together, they sum up to 180 degrees.
5. Exterior Angles: The exterior angles of an equilateral triangle are each equal to 120 degrees. The exterior angle is the supplementary angle to the interior angle.

Usage and Application:
- Equilateral triangles are used in various fields of study, including mathematics, art, and engineering.
- In mathematics, equilateral triangles serve as a basis for understanding geometric principles and properties.
- In art, equilateral triangles are often used to create symmetrical and balanced compositions.
- In engineering and architecture, equilateral triangles can be utilized to create stable and strong structures.

In conclusion, an equilateral triangle is a special type of triangle where all three sides are of equal lengths. It possesses symmetry, has interior angles measuring 60 degrees each, and is a fundamental concept in geometry. Understanding the properties and characteristics of an equilateral triangle is important in various fields of study and practical applications.

QR because in a right angled triangle hypotenuse is the biggest line and here point P is 90 degrees so the QR line would make hypotenuse

Correct answer is option d because:-

Total perimeter of the triangle is 180 degree
= x+50+60=180
50+60=110
110-180
=70 degree

So please this is explained answer please followed.

please

Understanding the Triangle Inequality Theorem

The statement in the question refers to the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is a fundamental concept in geometry and is applicable to all types of triangles, including equilateral, isosceles, and scalene triangles.

Explanation of the Triangle Inequality Theorem

To understand why the sum of the lengths of any two sides is greater than the length of the third side, we need to consider the possible scenarios that can occur when constructing a triangle.

Scenario 1: The sum of the lengths of two sides is equal to the length of the third side
In this scenario, when the sum of the lengths of two sides of a triangle is equal to the length of the third side, the three sides are said to be in a straight line, and the triangle is called a degenerate triangle. In such a case, the triangle collapses into a line segment, and it is not considered a valid triangle.

Scenario 2: The sum of the lengths of two sides is less than the length of the third side
In this scenario, when the sum of the lengths of two sides is less than the length of the third side, it is impossible to construct a triangle. When we try to connect the two shorter sides, they will not meet to form a closed figure.

Scenario 3: The sum of the lengths of two sides is greater than the length of the third side
In this scenario, when the sum of the lengths of two sides is greater than the length of the third side, it is possible to construct a triangle. When we try to connect the two shorter sides, they will meet to form a closed figure, and all three sides will be connected.

Conclusion

Based on the Triangle Inequality Theorem, we can conclude that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is essential in determining whether a given set of side lengths can form a valid triangle or not. Therefore, option 'A' - greater than, is the correct answer.

Understanding the Right-Angled Triangle
In a right-angled triangle, if the two legs are equal, we can refer to them as 'x'. According to the Pythagorean theorem, the relationship between the legs and the hypotenuse is given by:
- Hypotenuse² = Leg₁² + Leg₂²
Since both legs are equal:
- Hypotenuse² = x² + x²
- Hypotenuse² = 2x²
Given Information
We know that the square of the hypotenuse is 100 square units:
- 2x² = 100
Solving for x
To find the length of each leg, follow these steps:
1. Divide both sides by 2:
- x² = 100 / 2
- x² = 50
2. Now, take the square root of both sides to find 'x':
- x = √50
- x = √(25 * 2)
- x = 5√2
Conclusion
Thus, the length of each leg of the triangle is 5√2 units. Therefore, the correct answer is:
Option 'B': 5√2 units