Geometry is a branch of mathematics that focuses on the study of shapes, sizes, and relative positions of figures and shapes in space. It has been used for centuries to describe and measure the world around us. Geometry can be used to solve problems in many fields including engineering, architecture, art, and navigation. At its …
Compasses are a key tool in geometry, as they are used to draw circles and measure distances on a flat surface or plane. A compass is a simple instrument that consists of two hinged legs, with a pointed end on one leg and a pencil or pen on the other. The pointed end is used …
Angles are an important concept in geometry, as they are used to measure the size of the space between two lines or rays that have the same endpoint. The endpoint is called the vertex of the angle, and the lines or rays are called the sides of the angle. Angles are measured in degrees, with …
Plane geometry is a branch of mathematics that deals with the study of geometric shapes and their properties, which lie on a flat surface or plane. It is one of the oldest branches of mathematics, dating back to ancient civilizations such as the Greeks and the Egyptians. One of the fundamental concepts in plane geometry …
Geometry is a branch of mathematics that deals with shapes, sizes, and the properties of space. One common method of proving geometric statements is through the use of two-column geometry proofs. In a two-column proof, you start by stating a given or a theorem, and then proceed to prove it by presenting a series of …
In geometry, altitude refers to the perpendicular distance between a point and a reference plane. This concept is commonly used when discussing right triangles, where the altitude is the length of the line segment that is perpendicular to the triangle’s hypotenuse and intersects with the hypotenuse at its midpoint. The concept of altitude is important …
Circle theorems are mathematical statements that describe the properties of circles and their relationships to other geometric shapes. These theorems are used to solve problems involving circles and to understand the properties of circles and their relationships to other geometric shapes. One of the most fundamental circle theorems is the circle theorem that states that …
Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles. It is an important branch of mathematics that is used in a variety of fields, including physics, engineering, and computer science. One of the fundamental concepts in trigonometry is that of a right triangle. …
In geometry, transformations are changes that are made to a geometric shape or figure. There are several types of transformations that can be applied to a geometric shape, including translations, rotations, reflections, and dilations. A translation is a transformation that involves moving a shape to a new location on the same plane without changing its …
High school geometry and college level geometry are two very different forms of mathematics. Although both involve the same fundamental concepts, there are several key differences between the two. High school geometry focuses on basic concepts such as lines, angles, shapes, and theorems, while college level geometry encompasses more advanced topics such as non–Euclidean geometry …
High School Geometry VS College Level Geometry: What’s The Difference? Read More »
Coordinate geometry, also known as analytic geometry, is a branch of mathematics that focuses on the study of points, lines, angles, surfaces, and shapes in two-dimensional and three-dimensional space. It is a fundamental tool used to solve many real-world problems, such as finding the area of a triangle or the volume of a cylinder. The …
Geometry is a branch of mathematics that focuses on shapes, sizes, and relative positions of objects. It is used in a variety of everyday applications like constructing buildings, measuring distances, and even drawing maps. Geometry also has numerous rules and principles that must be followed in order to solve problems and make accurate calculations. One …
An angle bisector is a line or line segment that divides an angle into two equal parts. Angle bisectors are an important concept in geometry, and can be used to solve a variety of problems. The most basic way to understand an angle bisector is to think of it as a line that divides an …
A perpendicular bisector is a line that is perpendicular to (at a right angle to) and divides a line segment into two equal parts. In other words, it is a line that cuts a line segment in half so that the two halves are of equal length. It is also sometimes referred to as a …
Slope Intercept is an equation used to describe the linear relationship between two variables, x and y. It is written in the form y = mx + b, where m is the slope and b is the intercept. The slope is a value that represents the rate of change in the y–value relative to the …
Geometry is not just a branch of mathematics , it is also part of what surrounds us. The screen in front of you, isn’t it a rectangle? Don’t our bodies, for example, have different types of lines and angles ? Some more straight, others more curved; but straight lines and curved lines, after all. We will dedicate this post specifically to lines and angles . Undoubtedly, geometry is one …
Theorem 1 (Angle, angle determination theorem) In $\triangle ABC$ and $\triangle A’B’C’$, if $\angle A = \angle A’$, $\angle B = \angle B’$, then $\triangle ABC \xs \triangle A’B’C’$.△ABC△ABCand△A‘B‘C‘△A′B′C′in, if∠A=∠A‘∠A=∠A′,∠B=∠B‘∠B=∠B′,but△ABC △A‘B‘C‘△ABC△A′B′C′. prove According to the proportional theorem of common angles , note that $\angle C = \angle C’$, there are:∠C=∠C‘∠C=∠C′,Have: S△ABCS△A‘B‘C‘=AB⋅ACA‘B‘⋅A‘C‘=AB⋅BCA‘B‘⋅B‘C‘=AC⋅BCA‘C‘⋅B‘C‘S△ABCS△A′B′C′=AB⋅ACA′B′⋅A′C′=AB⋅BCA′B′⋅B′C′=AC⋅BCA′C′⋅B′C′thereby ACA‘C‘=BCB‘C‘=ABA‘B‘ACA′C′=BCB′C′=ABA′B′Therefore △ABC △A‘B‘C‘△ABC△A′B′C′ Theorem 2 (Edge, angle, …
Judgment Theorem for Similarity of Triangle Angles Read More »
Two parallel lines form angles with a transversal … ” Have you always heard this statement of Euclidean geometry and want to learn how it is demonstrated and what are its applications? You are in the right video lesson ! You have learned what parallel lines are and how they are defined, now you can learn the parallel lines …
l1:ax+by+c1=0 l2:ax+by+c2=0 The distance is: the absolute value of (c1-c2) divided by the square root (a square plus b square) Distance formula: d=|C1-C2|/√(A^2+B^2) The origin of the formula: Let the two straight line equations be Ax+By+C1=0, Ax+By+C2=0. The distance between two parallel straight lines is the distance from any point on one straight line to another …
Theorem 1 Two lines perpendicular to the same line are parallel. Theorem 2 Parallel lines are equidistant everywhere. Theorem 3 Two parallel straight lines are intercepted by a third straight line, and the interior angles are equal. Proof: Theorem 1 straight linel1⊥l3l1⊥l3，l2⊥l3l2⊥l3, to prove:l1 l2l1l2. Prove by contradiction. As shown in the figure: Assumptionl1l1andl2l2not parallel, straightl3l3hand over separatelyl1l1，l2l2AtAA，BB, you can …
