Question

prove SSS congruency criteria

Answer 1

Side-Side-Side (SSS) Rule

Side-Side-Side is a rule used to prove whether a given set of triangles are congruent.

The SSS rule states that:

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ.

sss rule

Answer 2

Hiii friend........

HERE IS UR ANSWER..........

""Proving congruent triangles with SSS.
Side side side postulate states that if three sides of one triangle are congruent to three sides of other triangle then these two triangles are congruent.""

→→Given triangles,
PQR and XYZ

such that

PQ =XY,

QR=YZ,

and PR= XZ

→→→To prove
Triangle PQR ~= XYZ

→→→Construction
Draw XW Intersecting YZ

such that

AngleWYZ =angle PQR

and
WY=PQ
Join WZ also

→→→Proof
In trianglePQR and triangleWYZ,,

PQ=WY (by construction)
angle PQR = angle WYZ (by construction)
QR= YZ (given)
TrianglePQR =triangle WYZ(sAS congruence)

Thus,
angle W= angle P(cpct).......(1)

In triangle XYW,
since,

PQ=YW ( by construction)

And
PQ,=XY

therefore

WY=XY

=>angle 1= angle 2
(angle opposite to equal sides are equal).......(2)

Similarly we can prove.
Angle 3 =angle 4..........(3)

Adding equation (2)&(3)
we get

=>Angle 1 + angle3= Angle2+ angle4

=>angle X= angle W

Now
from equation (1)

angle w= angle P

Therefore
angle P= angleX............(4)

Now in triangle PQR and XYZ

PQ=XY (given)

AngleP =angle X (equation 4)

PR=XZ(given)

Triangle PQR~= triangle XYZ ( SAS congruencey)


HENCE PROVED

THANKS FOR ASKING DUDU