9. What is conqruent of triangle? What are the criteria for Congruent of triangles.
Answers
SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
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❦Congruence of Triangles
Two triangles are said to be congruent if all their three sides and three angles are equal. But it is necessary to find all six dimensions. Hence, the congruence of triangles can be evaluated by knowing only three values out of six. The meaning of congruent in Maths is when two figures are similar to each other based on their shape and size. Also, learn about Congruent Figures here.
Congruence is the term used to define an object and its mirror image. Two objects or shapes are said to be congruent if they superimpose on each other. Their shape and dimensions are the same. In the case of geometric figures, line segments with the same length are congruent and angle with the same measure are congruent.
✌Conditions for Congruence of Triangles:
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA (Angle-Side-Angle)
- AAS (Angle-Angle-Side)
- RHS (Right angle-Hypotenuse-Side)
☛CPCT is the term, we come across when we learn about the congruent triangle. Let’s see the condition for triangles to be congruent with proof.
✔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 the same length and angles have same measure. Thus two triangles can be superimposed side to side and angle to angle.
✌Congruence Of Triangles
❥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.
❥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.
❥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.
❥AAS (Angle-Angle-Side)
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.
❥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.