Mariya kaviya risshoni

  Geometry is an important part of mathematics that deals with different shapes and figures. Triangles are an important part of geometry and the mid-point theorem points towards mid points of the triangle. What is Mid-Point Theorem? This theorem states that”  The line segment joining mid-points of two sides of a   triangle is parallel to the third side of the   triangle and is half of it” Proof of Mid-Point Theorem A triangle ABC in which D is the mid-point of AB and E is the mid-point of AC. To Prove:  DE ∥ BC and DE = 1/2(BC) Construction Extend the line segment joining points D and E to F such that DE = EF and join CF. Proof In ∆AED and ∆CEF  DE = EF (construction) ∠1 = ∠2 (vertically opposite angles) AE = CE (E is the mid-point) △AED ≅ △CEF by SAS criteria Therefore,  ∠3 =∠4 (c.p.c.t) But these are alternate interior angles. So, AB ∥ CF AD = CF(c.p.c.t) But AD = DB (D is the mid-point) Therefore, BD = CF In BCFD BD∥ CF (as AB ∥ CF) BD = CF BCF...

  Geometry - Definition with Examples What is Geometry? Geometry is a branch of mathematics that studies the  sizes , shapes, positions  angles  and dimensions of things. Flat  shapes  like squares, circles, and triangles are a part of flat geometry and are called 2D shapes. These shapes have only  2 dimensions , the length and the width. Examples of 2D shapes in flat geometry     Solid objects are also known as 3D objects having the third dimension of  height  or depth. Examples of 3D shapes in solid geometry   Angle : The  vertex  of a shape where two edges meet form an angle. Different shapes in geometry have different angle measures. For example : A triangle is a 3 sided shape, and the measure of its 3 interior angles is 180˚ A square, rectangle or quadrilateral are 4 sided shapes, and the measure of their interior angles is 360˚ Other polygons like the pentagon, hexagon, heptagon, octagon have 5, 6, 7, 8 sides re...

  Trigonometry  (from Greek trigonon "triangle" + metron "measure") Want to learn Trigonometry? Here is a quick summary. Trigonometry  ... is all about  triangles. Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more! Right-Angled Triangle The triangle of most interest is the  right-angled triangle . The right angle is shown by the little box in the corner: Another angle is often labeled  θ , and the three sides are then called: Adjacent : adjacent (next to) the angle  θ Opposite : opposite the angle  θ and the longest side is the  Hypotenuse   Why a Right-Angled Triangle? Why is this triangle so important? Imagine we can measure along and up but want to know the direct distance and angle: Trigonometry can find that missing angle and distance. Or maybe we have a distance and angle and need to "plot the dot" along and up: Questions like these are common in engineering, computer ...

  In   statistics , a   central tendency   (or   measure of central tendency ) is a central or typical value for a   probability distribution . [1] Colloquially, measures of central tendency are often called  averages .  The term  central tendency  dates from the late 1920s. [2] The most common measures of central tendency are the  arithmetic mean , the  median , and the  mode . A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the  normal distribution . Occasionally authors use central tendency to denote "the tendency of quantitative  data  to cluster around some central value." [2] [3] The central tendency of a distribution is typically contrasted with its  dispersion  or  variability ; dispersion and central tendency are the often characterized properties of distributions. Analysis may judge whether data has a strong or a weak c...

  Statistics   is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of   data . [1] [2] [3]   In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a   statistical population   or a   statistical model   to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of   surveys   and   experiments . [4] The  normal distribution , a very common  probability density , useful because of the  central limit theorem . Scatter plots  are used in descriptive statistics to show the observed relationships between different variables, here using the  Iris flower data set . When  census  data cannot be collected, ...