Question

What are the criteria for congruency and elaborate them well

Answer 1

hi there »»»»»»»ur answer friend..
1)SSS (side side side)
IN this criterai of congurency all sides of two triangels is same...
2)SAS(side angel side)
IN this criterai two sides and one angel between them is same...
3)AAS(angel angel side)
IN this criteria two angels along with one side is same....
4)RHS(Right angel hypotenuse side).
it is a case for right angel triangel when hypotenuse perpendicular and 90° are same ..
5)ASA(angel side angel)
when angels and side are same
THIS ATTACHMENT MAY HELP U

Answer 2

hey 
plz mark as brain list



This criterion for triangle congruence is one of our axioms. So we do not prove it but use it to prove other criteria. ... If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent

Side-Angle-Side (SAS)

This criterion for triangle congruence is one of our axioms. So we do not prove it but use it to prove other criteria.

Using words:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.

Using labels:

If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.

Side-Side-Side (SSS)

Using words:

If 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.

Using labels:

If in triangles ABC and DEF, AB = DE, BC = EF, and CA = FD, then triangle ABC is congruent to triangle DEF.

Proof: This was proved by using SAS to make "copies" of the two triangles side by side so that together they form a kite, including a diagonal. Then using what was proved about kites, diagonal cuts the kite into two congruent triangles.

Details of this proof are at this link. The similarity version of this proof is B&B Principle 8.

Angle-Side-Angle (ASA)

Using words:

If two angle in one triangle is congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

Using labels:

If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AB = DE, then triangle ABC is congruent to triangle DEF.

Proof: This proof was left to reading and was not presented in class. Again, one can make congruent copies of each triangle so that the copies share a side. Then one can see that AC must = DF.

For the proof, see this link. The similarity version of this proof is B&B Principle 6.

Side-Side-Angle (SSA) not valid in general

Using labels:

SSA would mean for example, that in triangles ABC and DEF, angle A = angle D, AB = DE, and BC = EF.

With these assumptions, it is not true that triangle ABC is congruent to triangle DEF. In general, there are two sets of congruent triangles with the same SSA data.

Examples were investigated in a class by a construction experiment. There is also a Java Sketchpad page that shows why SSA does not work in general.

Hypotenuse-Leg (HL) for Right Triangles

There is one case where SSA is valid, and that is when the angles are right angles.

Using words:

In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Using labels

If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.