Question

state the criterias for congruence of triangle and explain them with the help of figure. ​

Answer 1

Step-by-step explanation:

Required Answer :

A polygon made of three line segments forming three angles is known as a Triangle.

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

Criteria 1 : SSS (Side Side Side)

This criteria states that if all 3 sides of both the coresponding triangles are same they are said to be congruent by the rule SSS.

Example :

• Consider two triangles ∆ABC & ∆PQR
• AB = PQ
• QR = BC
• AC = PR
• Hence, the ∆ABC ≅ ∆PQR.

Criteria 2 : SAS (Side Angle Side)

If any two sides and the 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.

Example :

• Consider two triangles ∆ABC & ∆PQR
• AB = PQ,
• AC = PR
• ∠A = ∠P.
• Hence, Δ ABC ≅ Δ PQR.

Criteria 3 : ASA ( Angle Side Angle)

If any two angles and the 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.

Example :

• Consider two triangles ∆ABC & ∆PQR
• ∠B = ∠Q
• ∠C = ∠R
• BC = QR
• Hence, Δ ABC ≅ Δ PQR.

Criteria 4 : AAS (Angle-Angle-Side) [Application of ASA]

AAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

Example :

• Consider two triangles ∆ABC & ∆PQR
• ∠B = ∠Q [Corresponding sides]
• ∠C = ∠R [Corresponding sides]
• AC = PR [Adjacent sides]
• Hence, Δ ABC ≅ Δ PQR.

Criteria 5 : 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, then the two right triangles are said to be congruent by RHS rule.

• XZ = RT (Hypotenuse)
• YZ = ST (Side)
• Hence, ∆XYZ ≅ ∆RST.

Note : All the diagrams are in the attachment.!