1 what is Pythagoras theorem ?
2 what is algebra?
3 what is difference between fraction and rational number?
4 what is congruence?
please give me ans fast tomorrow has my examination please correct ans I will mark as brainlist please help me
Answers
Answer:
1. a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
2. a type of mathematics in which letters and symbols are used to represent numbers.
3. A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0. Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers).
4. agreement or harmony; compatibility.
Step-by-step explanation:
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Answer:
1 In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
Pythagorean theorem
The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
{\displaystyle a^{2}+b^{2}=c^{2},}a^{2}+b^{2}=c^{2},
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. The theorem, whose history is the subject of much debate, is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods - possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps, and cartoons abound.
2Algebra is one of the broad areas of mathematics. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0. ... Algebra is the branch of Maths which uses alphabetical letters to find unknown numbers. These letters are also called variables.
3 A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0. Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers).
4In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.[1]
An example of congruence. The two triangles on the left are congruent, while the third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants.
More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted.