What go congruence typical in mathematics?

In maths, two numbers are congruent if they have actually the exact same shape and also size, also though their place or orientation is different. The coincident parts of the congruent numbers are dubbed homologous or corresponding.

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How to know if 2 numbers space congruent?

Two integers a and also b are claimed to it is in congruent with respect to a organic number (positive integer) referred to as congruent modulo “m” if the divisions a/m and also b/m give the same remainder.

It’s written prefer this: a ≡ b mod (m).


What space congruent angles?

Two angles are said to be congruent if their equivalent sides and also angles space of same measure. 2 angles are likewise congruent if castle coincide once superimposed. That is, if by transforming it and/or moving it, they coincide through each other. The diagonals of a parallelogram also collection up congruent peak angles.

Congruence criteria for triangles

In many cases, it’s sufficient to establish the equality between three corresponding parts and use among the criteria come deduce the congruence of two triangles. The congruence criteria correspond to the postulates and also theorems the state which room the minimum problems that two or much more triangles must fulfill to it is in congruent. These are:

Congruence of your sidesCongruence of their angles 

For 2 triangles to it is in congruent, it’s enough that just some sides and also / or angles room equal.

SSS criterion

If you have two triangles and also the 3 sides that one are respectively congruent through those that the other, then the triangles are congruent. SSS stands for: side, side, side.

SAS criterion

Two triangles are congruent if 2 of your sides and the angle in between them space respectively equal. SAS stand for: side, angle, side.

ASA criterion

If two angles and the side between them room respectively congruent v the exact same of one more triangle, then the triangles space congruent. ASA stands for: angle, side, angle.

SSA criterion

Two triangles are congruent if they have actually two political parties respectively congruent and also the angle opposite the higher of the political parties are additionally congruent. SSA was standing for: side, side, angle.

What are surrounding angles?

An angle is a geometric figure that is developed with 2 rays the share the same vertex together an origin. Nearby is one adjective that describes what is located next to something.

Adjacent angles share a side and the vertex, while the various other two sides are opposite rays. This an interpretation allows you come infer that nearby angles are additionally contiguous or consecutive angles (because they have actually a common side and also the very same vertex) and supplementary angle (the sum of both results in 180°, i beg your pardon is well-known as a directly angle) .

Other nature of nearby angles is that their cosines have the exact same value, back they have inverse signs. For example, if you take it two adjacent angles, among 120° and also the other of 60°, the cosine the the very first is equal to the of the 2nd multiplied through -1. The sine of these angles, ~ above the various other hand, is the same.

What form of angles space congruent?

Vertical angles

When two lines intersect, 4 angles space formed. Those that room opposite each various other are upright angles, these are constantly congruent.

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How to uncover congruent angles?

You have the right to determine the congruence of triangle by making use of their angles in addition to the congruence of their sides. 2 triangles will certainly be equal if any of the following conditions are true:

If the three sides of two triangles A and B room equal, then they room congruent.If in 2 triangles A and B two of their sides and the angle formed by them are equal, then A and also B are congruent.If in 2 triangles A and B 2 of your angles space congruent and also the side in between them are equal, then A and B room congruent.

How to build a congruent angle?

It deserve to be very useful come know just how to build congruent angles, whether you’re illustration architectural diagrams or doing part trigonometry homework. To carry out this, friend must first draw one angle with a ruler and then usage a compass to copy the angle.

The crucial thing is to make sure they both keep the same angle, together this is the an interpretation of congruence. Follow these steps:

Mark a point with your pencil to designate the vertex of the first angle. You deserve to name that “A”.Set a right edge ruler so that it starts at A and also extends come the right.Draw a directly line native A to among the inch marks on the ruler, depending upon how long you desire to do it. You can mark the end of the line together “B”.Now, turn the rule. Make sure the beginning remains in ~ vertex “A”.Next, attract a directly line native “A” to one of the inch marks on the ruler, depending upon how lengthy you desire it. You can mark the chosen end as “C”.

Now, let’s see exactly how to build the congruent angles:

Mark a point with her pencil come designate the peak of the second angle. You have the right to mark it together “D”.Lay out a ruler so the it starts in ~ “D” and also extends to the right.Draw a right line native “D” to among the point out on the ruler, depending on the size you want. Note the chosen finish as “E”.Place the origin of your compass on the peak (“A”) of the an initial angle. Set the compass so the the end of the pencil is somewhere between “A” and “B.” note this allude as “L.”Draw an arc native the suggest on “AB” come the allude on the edge “AC”. You deserve to mark the point above “AC” as “M”.Take the compass without an altering the aperture, location it with its beginning at allude “D” and the end of the pencil at the allude of the edge “ED” it reaches. You can designate this point as “H”.Draw an arc from “H” the looks favor an arc that goes native “L” come “M”.Take the compass again, set its origin to “M” and collection it so that the end is in ~ “L”.Now, take it the compass, collection its beginning at “H”, and also rotate the pencil over the arc expanding from “H” till it touches the arc. Specify this suggest as “G”.Finally, position the leaf of the leader so that it starts in ~ “G” and extends toward “D.” attract a heat from “G” to “D”.

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