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CSAT > 26.Geometry > Flashcards

26.Geometry Flashcards

1
Q

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

A

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

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2
Q

How many types of triangles are there based on angles?

A

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

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3
Q

How many types of triangles are there based on sides?

A

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

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4
Q

What is the triangle inequality theorem?

A

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.

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5
Q

What is the difference between two sides of a triangle?

A

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

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6
Q

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

A

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

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7
Q

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

A

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

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8
Q

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

A

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

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9
Q

How do you find the perimeter of a triangle?

A

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

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10
Q

What is the semi-perimeter of a triangle?

A

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

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11
Q

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

A

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.

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12
Q

What is the inradius of a triangle?

A

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

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13
Q

What is the circumradius of a triangle?

A

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

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14
Q

How do you calculate the area of a triangle?

A

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

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15
Q

How is the area of a triangle calculated in trigonometry?

A

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.

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16
Q

What is the area of an equilateral triangle?

A

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

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17
Q

What are some important Pythagorean triplets?

A

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

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18
Q

What is a quadrilateral?

A

A quadrilateral is a polygon with four sides.

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19
Q

What is a trapezium?

A

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

20
Q

Name four special types of quadrilaterals.

A

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

21
Q

What is a quadrilateral?

A

A quadrilateral is a polygon with four sides.

22
Q

What is a trapezium?

A

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

23
Q

What is a parallelogram?

A

A parallelogram is a quadrilateral with opposite sides parallel.

24
Q

What are the properties of a parallelogram?

A

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.

25
Q

What is a rectangle?

A

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

26
Q

What are the properties of a rectangle?

A

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.

27
Q

What is a square?

A

A square is a rectangle with all sides equal in length

28
Q

What are the properties of a square?

A

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.

29
Q

What is a rhombus?

A

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

30
Q

What are the properties of a rhombus?

A

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.

31
Q

What is the formula for the perimeter of a quadrilateral?

A

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

32
Q

What is the formula for the area of a parallelogram?

A

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

33
Q

What is the formula for the area of a rectangle?

A

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

34
Q

What is the formula for the area of a square?

A

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

35
Q

What is the formula for the area of a rhombus?

A

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

36
Q

What is the formula for the diagonals of a rectangle?

A

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

37
Q

What is the formula for the diagonals of a square?

A

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

38
Q

What is the formula for the diagonals of a rhombus?

A

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.

39
Q

What are the angles in a square?

A

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

40
Q

What are the angles in a rhombus?

A

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

41
Q

Formulae for Quadrilaterals:

A

*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.

42
Q

Trapezium:

A

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.

43
Q

Parallelogram:

A

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.

44
Q

Rectangle:

A

*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.

45
Q

Square:

A

*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.

46
Q

Rhombus:

A

*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.

CSAT (26 decks)

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