# Geometry

## Factors and Multiples

Home Numbers & Operations Factors and multiples Factors and multiples worksheets We have numerous factors and multiples worksheets for elementary level. Factors and multiples go hand in hand but these concepts are different. Let’s get to know factors and multiples and the difference between them.  Factors: Consider the number 8. All the numbers which divide 8 completely without leaving any remainder are factors of 8. 1, 2, 4, and 8 divide 8 completely leaving no remainder. So the factors of 8 are 1, 2, 4, and 8.  Note: 1, and 8 are common factors. Thus, all the numbers have 1 and the number itself as common multiples.    So factors are numbers that exactly divide the given number without leaving any remainder. So the number which is to be divided is the ‘dividend’ and it’s exactly divided by another number which is the ‘divisor’ with zero as the remainder. The divisor is the dividend here.  Multiples: Multiples are again an easy concept to understand. To put it in simple words, the multiple of a number is the product of that number multiplied by another number(an integer).  From the above image the multiples of 10 are 20, 30, 40, 50, and so on. You can find the multiples of anything. It can either be a positive integer or a negative integer.  Difference between factors and multiples: S.No Factors Multiples 1 Factors are numbers that completely divide another number The product obtained by multiplying two numbers is a multiple. 2 Number of factors- finite Number of multiples- Infinite 3 Involves division of numbers Involves multiplication of numbers 4 The factors of a number are always lesser than or equal to the number The multiples of a number are always greater than or equal to the number Factors and multiples worksheets free download pdf

## Measuring Angles

Home Geometry Measuring Angles Measuring Angles worksheets Measuring angles is much easy after we started to use a  mathematical tool, the protractor. In these printable measuring angles worksheets, we will learn to measure angles using a protractor. We have already learnt that two rays originating from a common end point form an angle. The magnitude of an angle is the amount of rotation of one arm about the vertex to bring it to the position of the other arm. One complete rotation of a ray about a point is divided into 360 equal parts. Each part is considered 1° (one degree). Measuring an angle using a protractor in an anticlockwise direction:  This is measurement in anticlockwise direction. Thus, we will use the inner scale to measure the angle. The centre of the protractor is placed on the vertex B of the angle ABC. The base line of the protractor should coincide with the base BC of the angle. Read the markings where the arm BC overlaps the markings on the protractor. That measurement is the measure of the angle. Therefore, the angle ABC measures 45° The same procedure is followed for measuring an angle in the clockwise direction, but the outer scale is used here to measure the angle. Download all the worksheets and learn to measure angles in a simple way. Measuring Angles worksheets free download pdf

## Types of Angles

Home Geometry Types of Angles Worksheets Types of Angles Worksheets Worksheets on classification or types of angles are given in this section for Grade 5 and grade 6 students. The various types of angles are described with images on charts for easy understanding. You can print them for reference. How do you classify angles? Angles are simply classified according to their magnitudes. To make it easy, draw a circle. Divide it into 360 equal parts. Every single part is 1º (one degree). One complete rotation of a ray about a point is divided into 360 equal parts. Types of angles: Zero angle: Exactly measures 0º . Acute angle: Measures greater than 0º but less than 90º . Right abgle: Exactly measures 90º .   Obtuse angle: Measures greater than 90º  but less than 180º . Straight angle: Exactly measures 180º . Reflex angle: Measures greater than 180º  but less than 360º . Full angle or Complete angle: Exactly measures 360º . Also, refer the figures given below for clear understanding. More than 30 worksheets to find and name different types of angles. Download all worksheets and start practicing. Types of Angles free download pdf

## Pair of Angles

Home Geometry Angles Worksheets Pair of Angles Pair Of Angles Worksheets The previous sets of worksheets are on complementary and supplementary pairs of angles. http://mathfunworksheets.com/complementary-and-supplementary-angles/ Now, we will learn more pairs of angles for grade 6 to grade 8 like linear, vertically opposite and adjacent angles here. Before you know all these pairs of angles there is another important concept which is called ‘angles on a straight line’. The sum of angles on a straight line is 180 degree. Thus, any number of angles on a straight line amounts to 180 degree. Vertically opposite angles: Vertical angles or vertically opposite angles are opposite angles formed when two lines intersect each other. Thus, two pairs of opposite angles are formed when two lines intersect. Here, the pair of opposite angles are equal. Refer the figure given below for clear understanding.   Adjacent angles: Two angles are said to be adjacent, if they have a common vertex and a common arm. The angles should not overlap which means the other arms are lying on the opposite side of the common arm.   Linear pair of angles: Two adjacent angles whose sum is always 180 degree form a linear pair. They can also be called as supplementary angles.   All you need to do now is to just print all these worksheets and work on them. Only when you are thorough with these concepts, you can understand corresponding and alternate angles. Also, these pairs of angle are very important to find the missing measures of angles in interior and exterior angle concept. Identify and differentiate the different pairs of angles, find the missing measure of angles, solve equations and word problems in these free pintables. Examples are shown wherever necessary. RELATED GEOMETRY TOPICS  :  2D Shapes, 3D Shapes, Lines rays line segments and planes, Composing and Decomposing shapes Pair of Angles Worksheets

## Naming Angles Worksheets

Home Geometry Naming Angles Worksheets Naming Angles Worksheets An angle is formed when two rays or line segments meet at a common end point. You must be familiar with lines, rays, line segments, and planes before we learn to name angles. http://mathfunworksheets.com/lines-rays-line-segments-and-planes/ In these printable naming angles worksheets, you will learn to name angles in four different ways. The rules to name angles are given in detail in the charts below. The common meeting point of the angle is called the vertex. The two line segments or the two rays are the arms of the angle. The figure given below shows an angle with vertex and arms marked. The last set of worksheets given here deal with exterior and interior of the angle. All the points marked within the space enclosed by the arms are in the interior of the angle and the points marked outside the arms are in the exterior. Download all these worksheets to know all about angles which forms the base of triangles. Two Intercept Form worksheets free download pdf

## Composing and Decomposing Shapes

Home Geometry Composing and Decomposing Shapes Composing and Decomposing Shapes – Activity Worksheets Free worksheets on composing and decomposing shapes would definitely give elementary kids a clear understanding on 2 D, 3 D and composite shapes which form the basis of Geometry. Other topics that can addressed with the help of composing and decomposing shapes are fractions, proportions, area, and perimeter. Total surface area and volume are two important concepts when you deal with 3 D shapes. Composing is combining or joining two or more shapes to form a new shape. Decomposing, as the name implies, is the splitting or breaking a shape into two or more shapes. An example is illustrated below Decomposing a composite shape: When you have practiced all the worksheets here, you will easily use two-  dimensional shapes like squares, rectangles, triangles, trapezoids, circles and three- dimensional shapes like cubes, cuboids, hemispheres, right circular cones, rectangular pyramids to create composite shapes and also to create new shapes from composite shapes. Fun filled, logical thinking worksheets are here for free download. Think well before you build and break!!! Composing and Decomposing Shapes Printable Worksheets

## Angles in Triangles

Home Geometry Angles in Triangles Angles in Triangles Worksheets The angle formed between two adjacent sides of a triangle is called an interior angle. The sum of all of the measures of the interior angles in a triangle is 180∘. An angle formed between a side of the triangle and an adjacent side extending outward is called an exterior angle. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. In the above diagram a, b, and c are the interior angles. x, y, and z are the exterior angles Angles in Triangles worksheets free download pdf

## Triangle Inequality Theorem

Home Geometry Triangle Inequality Theorem Triangle Inequality Theorem Worksheets The Triangle Inequality theorem states that in a triangle, the sum of lengths of any two sides must be greater than the length of the third side. A triangle with sides of length a, b, and c, it must satisfy that a + b > c, a + c > b, and b + c > a. Triangle Inequality Theorem worksheets free download pdf

## Medians and Centroid of a triangle

Home Geometry Medians and Centroid of a triangle Medians and Centroid of a triangle Worksheets A Median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. The medians of a triangle are concurrent and they intersect in one common point. The Centroid of a triangle is the point of intersection of all the three medians of a triangle. The centroid always divides each median into two parts, in the ratio 2:1. Medians and Centroid of a triangle worksheets free download pdf

## Pythagorean Theorem

Home Geometry Pythagorean Theorem Pythagorean Theorem Worksheets What is Pythagorean Theorem? Pythagorean Theorem or Pythagoras Theorem states, “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides”. This can be expressed as c2 = a2 + b2; where ‘c’ is the hypotenuse and ‘a’ and ‘b’ are the two legs of the triangle. The Pythagorean theorem can be used to: To check if a triangle is right-angled To determine the speed of sound in the ocean by oceanographers To find the range and sound source by aerospace scientists and meteor. Two Intercept Form worksheets free download pdf

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