How do we understand that when to use S. S. S. congruence
S. A. S. conguence
A. S. A. conguence
R. H. S. congruence
please can anyone explain me
I will mark you as the brainliest
Answers
hey mate!
CONGRUENCE OF TRIANGLES
A polygon made of three line segments forming three angles is known as Triangle.
Two triangles are said to be congruent if their sides have same length and angles have same measure. Thus two triangles can be superimposed side to side and angle to angle.
Congruence Of Triangles
In the above figure, D ABC and D PQR are congruent triangles. This means,
Vertices: A and P, B and Q, and C and R are same.
Sides: AB=PQ, QR= BC and AC=PR;
Angles: Ð A = Ð P, ÐB = ÐQ and Ð C= Ð R.
Congruent triangles are triangles having corresponding sides and angles to be equal. Congruence is denoted by the symbol ≅. They have same area and same perimeter.
Congruence of triangles can be predicted without actually measuring the sides and angles. Different rules of congruence of triangles are as follows:
SSS (Side-Side-Side):
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
Congruence Of Triangles
In above given figure, AB= PQ, QR= BC and AC=PR, hence D ABC ≅ D PQR.
SAS (Side-Angle-Side):
If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.
Congruence Of Triangles
In above given figure, sides AB= PQ, AC=PR and angle between AC and AB equal to angle between PR and PQ i.e. Ð A = Ð P, hence D ABC ≅ D PQR.
ASA (Angle-Side- Angle)
If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
Congruence Of Triangles
In above given figure, Ð B = Ð Q, Ð C = Ð R and sides between Ð B and ÐC , Ð Q and Ð R are equal to each other i.e. BC= QR, hence D ABC ≅ D PQR.
RHS (Right angle- Hypotenuse-Side)
If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, the right triangles are said to be congruent by RHS rule.
Congruence Of Triangles
In above figure, hypotenuse XZ = RT and side YZ=ST, hence triangle XYZ ≅ triangle RST.