26.Geometry

Question 1

What is the sum of the three angles of a triangle?

Answer 1

The sum of the three angles of a triangle is always 180°.

Question 2

How many types of triangles are there based on angles?

Answer 2

There are three types of triangles based on angles: acute, obtuse, and right triangles.

Question 3

How many types of triangles are there based on sides?

Answer 3

There are three types of triangles based on sides: scalene, isosceles, and equilateral triangles.

Question 4

What is the triangle inequality theorem?

Answer 4

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Question 5

What is the difference between two sides of a triangle?

Answer 5

The difference between the lengths of any two sides of a triangle is always less than the length of the third side.

Question 6

What is the sum of the interior angles of a triangle?

Answer 6

The sum of the interior angles of a triangle is always 180°.

Question 7

What is the relationship between the exterior angle and the two opposite angles of a triangle?

Answer 7

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.

Question 8

What is the sum of the exterior angles of a triangle?

Answer 8

The sum of the exterior angles of any triangle is always 360°.

Question 9

How do you find the perimeter of a triangle?

Answer 9

The perimeter of a triangle is equal to the sum of the lengths of its three sides

Question 10

What is the semi-perimeter of a triangle?

Answer 10

The semi-perimeter of a triangle is half the sum of the lengths of its three sides.

Question 11

How do you calculate the area of a triangle using Heron’s formula?

Answer 11

The area of a triangle can be calculated using Heron’s formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, and c are the lengths of the sides.

Question 12

What is the inradius of a triangle?

Answer 12

The inradius of a triangle is the radius of the inscribed circle, which is tangent to all three sides of the triangle.

Question 13

What is the circumradius of a triangle?

Answer 13

The circumradius of a triangle is the radius of the circumcircle, which passes through all three vertices of the triangle.

Question 14

How do you calculate the area of a triangle?

Answer 14

The area of a triangle can be calculated using the formula: Area = (base * height) / 2.

Question 15

How is the area of a triangle calculated in trigonometry?

Answer 15

In trigonometry, the area of a triangle can be calculated using the formula: Area = (1/2) * a * b * sin(C), where a and b are the lengths of two sides, and C is the included angle.

Question 16

What is the area of an equilateral triangle?

Answer 16

The area of an equilateral triangle can be calculated using the formula: Area = (side^2 * √3) / 4.

Question 17

What are some important Pythagorean triplets?

Answer 17

Some important Pythagorean triplets are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Question 18

What is a quadrilateral?

Answer 18

A quadrilateral is a polygon with four sides.

Question 19

What is a trapezium?

Answer 19

A trapezium is a quadrilateral with one pair of parallel sides.

Question 20

Name four special types of quadrilaterals.

Answer 20

The four special types of quadrilaterals are parallelogram, rectangle, square, and rhombus.

Question 21

What is a quadrilateral?

Answer 21

A quadrilateral is a polygon with four sides.

Question 22

What is a trapezium?

Answer 22

A trapezium is a quadrilateral with one pair of parallel sides.

Question 23

What is a parallelogram?

Answer 23

A parallelogram is a quadrilateral with opposite sides parallel.

Question 24

What are the properties of a parallelogram?

Answer 24

The properties of a parallelogram are: opposite sides are parallel, opposite sides are equal in length, opposite angles are equal, and consecutive angles are supplementary.

Question 25

What is a rectangle?

Answer 25

A rectangle is a parallelogram with all angles equal to 90 degrees.

Question 26

What are the properties of a rectangle?

Answer 26

The properties of a rectangle are: all angles are right angles (90 degrees), opposite sides are equal and parallel, and diagonals are equal in length.

Question 27

What is a square?

Answer 27

A square is a rectangle with all sides equal in length

Question 28

What are the properties of a square?

Answer 28

The properties of a square are: all angles are right angles (90 degrees), all sides are equal in length, and diagonals are equal and bisect each other at right angles.

Question 29

What is a rhombus?

Answer 29

A rhombus is a parallelogram with all sides equal in length.

Question 30

What are the properties of a rhombus?

Answer 30

The properties of a rhombus are: opposite sides are parallel, all sides are equal in length, opposite angles are equal, and diagonals bisect each other at right angles.

Question 31

What is the formula for the perimeter of a quadrilateral?

Answer 31

The perimeter of a quadrilateral is the sum of the lengths of its four sides.

Question 32

What is the formula for the area of a parallelogram?

Answer 32

The area of a parallelogram is the product of the base length and the height.

Question 33

What is the formula for the area of a rectangle?

Answer 33

: The area of a rectangle is the product of its length and width.

Question 34

What is the formula for the area of a square?

Answer 34

The area of a square is the square of its side length.

Question 35

What is the formula for the area of a rhombus?

Answer 35

The area of a rhombus is the product of its diagonals divided by 2.

Question 36

What is the formula for the diagonals of a rectangle?

Answer 36

The diagonals of a rectangle are equal in length and can be calculated using the Pythagorean theorem.

Question 37

What is the formula for the diagonals of a square?

Answer 37

The diagonals of a square are equal in length and can be calculated using the side length of the square.

Question 38

What is the formula for the diagonals of a rhombus?

Answer 38

The diagonals of a rhombus are perpendicular bisectors of each other and can be calculated using the side length and one angle of the rhombus.

Question 39

What are the angles in a square?

Answer 39

All angles in a square are right angles (90 degrees).

Question 40

What are the angles in a rhombus?

Answer 40

Opposite angles in a rhombus are equal, but they are not necessarily right angles.

Question 41

Formulae for Quadrilaterals:

Answer 41

*Perimeter of a Quadrilateral: P = a + b + c + d, where a, b, c, and d are the lengths of the four sides. *Area of a Quadrilateral (Using Brahmagupta's Formula): A = √((s - a)(s - b)(s - c)(s - d)), where s is the semi-perimeter and a, b, c, and d are the lengths of the sides.

Question 42

Trapezium:

Answer 42

Area of a Trapezium: A = ½(b1 + b2)h, where b1 and b2 are the lengths of the parallel sides and h is the height.

Question 43

Parallelogram:

Answer 43

Area of a Parallelogram: A = base × height, where the base is the length of one of the parallel sides and the height is the perpendicular distance between the parallel sides.

Question 44

Rectangle:

Answer 44

*Perimeter of a Rectangle: P = 2(length + width), where length and width are the measurements of the sides. *Area of a Rectangle: A = length × width, where length and width are the measurements of the sides.

Question 45

Square:

Answer 45

*Perimeter of a Square: P = 4s, where s is the length of one side. *Area of a Square: A = s², where s is the length of one side. *Diagonal of a Square: d = s√2, where s is the length of one side.

Question 46

Rhombus:

Answer 46

*Perimeter of a Rhombus: P = 4s, where s is the length of one side. *Area of a Rhombus: A = (d1 × d2) / 2, where d1 and d2 are the lengths of the diagonals. *Diagonal of a Rhombus: d = √(s₁² + s₂²), where s₁ and s₂ are the lengths of the sides.