Students can go through AP Board 7th Class Maths Notes Chapter 8 Congruency of Triangles to understand and remember the concepts easily.
AP State Board Syllabus 7th Class Maths Notes Chapter 8 Congruency of Triangles
→ Two figures are said to be identical if their shapes are same.
Eg: Any two squares, circles or equilateral triangles.
→ Two figures are said to be congruent if they are identical in shape and equal in size.
→ Two line segments are congruent if they have same lengths.
→ Two triangles are congruent if the corresponding angles are equal.
→ We establish the congruency of the triangles by following criteria.
→ S.S.S. criterion: If three sides of a triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.
FA = TI; AN = IN; FN = TN then △FAN ≅ △TIN
→ S.A.S. criterion: If two sides and the angle included between the two sides of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent.
CA = PI; ∠C = ∠P; CT = PG
then, △CAT ≅ △PIG
→ A.S.A. criterion : If two angles and the included side of a triangle are equal to the corresponding two angles and included side of another triangle then the triangles are congruent.
∠A = ∠I; AT = IM; ∠T = ∠M then △MAT ≅ △DIM.
→ R.H.S. criterion: In two right angled triangles, if the hypotenuse and one corresponding side are equal then they are congruent.
∠B = ∠E = 90°
BC = EF
AC = DF
then △ABC ≅ △DEF
→ If by any criterion two triangles are congruent then all the corresponding parts are equal.