26.Geometry Flashcards
What is the sum of the three angles of a triangle?
The sum of the three angles of a triangle is always 180°.
How many types of triangles are there based on angles?
There are three types of triangles based on angles: acute, obtuse, and right triangles.
How many types of triangles are there based on sides?
There are three types of triangles based on sides: scalene, isosceles, and equilateral triangles.
What is the triangle inequality theorem?
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.
What is the difference between two sides of a triangle?
The difference between the lengths of any two sides of a triangle is always less than the length of the third side.
What is the sum of the interior angles of a triangle?
The sum of the interior angles of a triangle is always 180°.
What is the relationship between the exterior angle and the two opposite angles of a triangle?
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
What is the sum of the exterior angles of a triangle?
The sum of the exterior angles of any triangle is always 360°.
How do you find the perimeter of a triangle?
The perimeter of a triangle is equal to the sum of the lengths of its three sides
What is the semi-perimeter of a triangle?
The semi-perimeter of a triangle is half the sum of the lengths of its three sides.
How do you calculate the area of a triangle using Heron’s formula?
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.
What is the inradius of a triangle?
The inradius of a triangle is the radius of the inscribed circle, which is tangent to all three sides of the triangle.
What is the circumradius of a triangle?
The circumradius of a triangle is the radius of the circumcircle, which passes through all three vertices of the triangle.
How do you calculate the area of a triangle?
The area of a triangle can be calculated using the formula: Area = (base * height) / 2.
How is the area of a triangle calculated in trigonometry?
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.
What is the area of an equilateral triangle?
The area of an equilateral triangle can be calculated using the formula: Area = (side^2 * √3) / 4.
What are some important Pythagorean triplets?
Some important Pythagorean triplets are (3, 4, 5), (5, 12, 13), and (8, 15, 17).
What is a quadrilateral?
A quadrilateral is a polygon with four sides.
What is a trapezium?
A trapezium is a quadrilateral with one pair of parallel sides.
Name four special types of quadrilaterals.
The four special types of quadrilaterals are parallelogram, rectangle, square, and rhombus.
What is a quadrilateral?
A quadrilateral is a polygon with four sides.
What is a trapezium?
A trapezium is a quadrilateral with one pair of parallel sides.
What is a parallelogram?
A parallelogram is a quadrilateral with opposite sides parallel.
What are the properties of a parallelogram?
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.
What is a rectangle?
A rectangle is a parallelogram with all angles equal to 90 degrees.
What are the properties of a rectangle?
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.
What is a square?
A square is a rectangle with all sides equal in length
What are the properties of a square?
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.
What is a rhombus?
A rhombus is a parallelogram with all sides equal in length.
What are the properties of a rhombus?
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.
What is the formula for the perimeter of a quadrilateral?
The perimeter of a quadrilateral is the sum of the lengths of its four sides.
What is the formula for the area of a parallelogram?
The area of a parallelogram is the product of the base length and the height.
What is the formula for the area of a rectangle?
: The area of a rectangle is the product of its length and width.
What is the formula for the area of a square?
The area of a square is the square of its side length.
What is the formula for the area of a rhombus?
The area of a rhombus is the product of its diagonals divided by 2.
What is the formula for the diagonals of a rectangle?
The diagonals of a rectangle are equal in length and can be calculated using the Pythagorean theorem.
What is the formula for the diagonals of a square?
The diagonals of a square are equal in length and can be calculated using the side length of the square.
What is the formula for the diagonals of a rhombus?
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.
What are the angles in a square?
All angles in a square are right angles (90 degrees).
What are the angles in a rhombus?
Opposite angles in a rhombus are equal, but they are not necessarily right angles.
Formulae for Quadrilaterals:
*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.
Trapezium:
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.
Parallelogram:
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.
Rectangle:
*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.
Square:
*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.
Rhombus:
*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.
