What do congruent and similar mean in maths?

Answer 1

If ur talking abt shapes such as triangles then:
congruent triangles are those
which have the same corresponding
angles and same length of corresponding sides.
Similar triangles r those which have the same
corresponding angles and
the same ratio b/w their corresponding sides
but not the same length.

Answer 2

Let us take two triangles to
clearly bring out the meaning.
1]Two two triagles are similar if all 3 angles in one
are equal to the corresponding angles in the other. Sides need not be equal.
2]Two triangles are congruent if one can be
exactly laid over he other. All of the 3 angles and sides are equal to the corresponding angles and sides.

Answer 3

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification (Coxeter and Greitzer 1967, p. 94). A transformation that takes figures to similar figures is called a similarity.

Two figures are directly similar when all corresponding angles are equal and described in the same rotational sense. This relationship is written . (The symbol is also used to mean "is the same order of magnitude as" and "is asymptotic to.") Two figures are inversely similar when all corresponding angles are equal and described in the opposite rotational sense.

Two triangles are similar if:

two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent).
the three pairs of corresponding sides are proportional.
Two triangles are congruent if:

all 6 pairs of corresponding angles and sides are congruent.
If all 3 pairs of corresponding sides in two triangles are the same, then the triangles are congruentSSS
Try to connect the points labeled B in the broken triangles. Can you make triangles that aren't congruent?

If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent.

source: Geometry: Congruent Triangles

Press "r" to reset the sketch on the right.




Source: Cheng Wing Kuen's Pythapf.gsp

ASA
Try to connect the points labeled C in the broken triangles. Can you make triangles that aren't congruent?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

ASA
Try to connect the points labeled C in the broken triangles. Can you make triangles that aren't congruent?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

source: Geometry: Congruent Triangles




AAS
Try to connect the points labeled C in the broken triangles. Can you make triangles that aren't congruent?

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, the two triangles are congruent.

source: Geometry: Congruent Triangles

Press "r" to reset the sketch on the right.




source: Cheng Wing Kuen's Pythapf.gsp

Hyp-S
If the hypotenuse and the leg of one right triangle are congruent to the corresponding parts of the second right triangle, the two triangles are congruent




SSA
How many triangles can be formed given two sides and the angle not between them?

Try to connect the points labeled B in the broken triangles. Can you create two non-congruent triangles?

Two triangles with two sides and a non-included angle equal may or may not be congruent.

Press "r" to reset the sketch on the right.


source: Cheng Wing Kuen's Pythapf.gsp

AAA
How many triangles can be formed given three angles?

Drag points A and B in the triangle. Does the triangle maintain its shape and size?

(Angles A and B determine angle C)

If two angles on one triangle are equal, respectively, to two angles on another triangle, then the triangles are similar, but not necessarily congruent.

When you learn the mathematics of similar triangles, you can you use the knowledge to determine unknown dimensions or angles without measuring. You have already explored the angle relationships of similar triangles. If you know an angle in one triangle, the corresponding angle in a similar triangle will be the same size.

Answer 4

congruent means the same shape AND size,
similar shapes are in the same proportion but can be different size.
eg. a 3cm square is only congruent to another 3cm square, but can be similar to any other square, because the shape is preserved, only the size is different

Answer 5

They are two separate terms in geometry
Congruent means they exactly fit each other
Example if you draw two triangles with sides 4 5 and 3 units each whichever way you draw them they will fit each other - example you draw both of them on a piece of a paper & cut both of them they will fit on each other one hiding the other
you will find theorems like hyp-side, hyp-angle, ASA, SAS, SSS, SAA (where S stands for side, A stands for Angle) for two traingles taken in given order - are used to confirm congruency in triangles. However congruency can be applicable for other figures also.for eg two quadrilaterals or two pentagons also can be congruent
The other term Similar literally means looks alike like two identical photographs of same person printed in different sizes.
take for eg two equilateral triangles (all angles =60 deg)
one of side 6 cm each and another 10 cm each will be similar to each other. Both the triangles are not congruent.
In two similar triangles unlike in congruent triangles the sides are in proportion . eg: a triangle with sides 10 and 8 with angle 60 deg in between the two sides is similar to a triangle with side 5, 4 and angle 60deg between them.

please note that all congruent figures are similar but all similar figures are not necessarily congruent.

Subhash

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Answer 6

You got a trinagle ABC and DEF

If they are Congruent then their sides are same length (because of that their angles are also same)
AB = DE and BC = EF and AC = DF

If they are simillar thier sides are no longer same but the angles are still the same
ABC = DEF and BCA = EFD and CAB = FDE

Answer 7

One (4cmx4cm)square is similar to any other square but congruent only to another 4cmx4cm square.

Answer 8

congruent means suitable .consistent .having exactly the same size