What Do You Know About Geometry?

A diameter is a line segment that passes through the center of a circle and divides it into two equal halves. It is the longest chord in a circle and also the only chord that passes through the center. Therefore, the correct answer is diameter.

Euclid is considered the father of Geometry because he was a Greek mathematician who compiled and organized the fundamental principles of geometry in his book "Elements." This work, consisting of 13 books, covers various aspects of geometry and is considered one of the most influential mathematical texts in history. Euclid's systematic approach and logical proofs laid the foundation for the study of geometry and had a significant impact on the development of mathematics.

The line which joins the adjacent side and the opposite side of a right angle triangle is called the hypotenuse. The hypotenuse is the longest side of the triangle and it is opposite the right angle. It is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the correct answer is Hypotenuse.

A parallelogram with 4 right angles and 4 equal sides is called a square. A square is a special type of parallelogram where all angles are right angles and all sides are equal in length. This unique combination of properties distinguishes a square from other parallelograms such as a trapezium, rhombus, or rectangle.

An isosceles triangle has two sides that are equal in length. In an isosceles triangle, the two equal sides are opposite each other and the angles opposite the equal sides are also equal. Therefore, an isosceles triangle is the correct answer for a triangle with two equal sides.

The formula Length x Breath x Height is used to calculate the volume of a cuboid. A cuboid is a three-dimensional shape with six rectangular faces, and its volume represents the amount of space it occupies. By multiplying the length, breadth, and height of the cuboid, we can determine its total volume. This formula is not applicable to the other options provided, as they involve different shapes and calculations.

Geometry is useful in various fields such as engineering, medicine, and art and architecture. However, it is not directly applicable in the field of law. While law may involve analyzing and interpreting various forms of evidence, geometry is not typically used in this process. Instead, legal professionals rely on legal principles, statutes, case law, and legal reasoning to make their arguments and reach decisions. Therefore, geometry is not considered as essential in the field of law as it is in the other mentioned fields.

A geometer is someone who studies geometry. Geometry is a branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and solids. Geometers explore the concepts and principles of geometry, such as shapes, measurements, and spatial relationships. They may use mathematical formulas and proofs to analyze and solve geometric problems. Therefore, the correct answer is geometer.

Polygons are shapes with more than 4 angles and sides. A polygon can have any number of sides greater than 4, such as pentagon, hexagon, heptagon, etc. Therefore, the correct answer is polygons.

The non-Euclidean geometry was discovered in the 19th century. During this time period, mathematicians such as Carl Friedrich Gauss, Nikolai Lobachevsky, and János Bolyai developed and explored geometries that did not adhere to Euclid's axioms. These new geometries challenged the assumption that parallel lines never intersect and opened up new possibilities for understanding space and geometry. The 19th century was a pivotal time for the development of non-Euclidean geometry and marked a significant shift in mathematical thinking.