CONGRUENCE OF TRIANGLES - ESSENTIAL POINTS
- Congruence: The relation of two objects being congruent is called congruence. Congruent objects are exact copies of one another.
- Congruence of Plane Figures: The method of superposition examines the congruence of plane figures. Two planes figures say F1 and F2 are said to be congruent, if the trace-copy of F1 fits exactly on that of F2. We write this as F1 ≅
- Congruence of Line Segments: Two line segments, say AB and CD, are congruent, if they have equal lengths. AB = CD.
- Congruence of Angles: Two angles, ∠1 and ∠2 are congruent, if their measures are equal. We write this as ∠1 ≅ ∠2 or as m ∠1 = m ∠2 or simply as ∠1 = ∠
- Congruent objects are exact duplicates of one another.
- The method of superposition examines the congruence of plane figures. If two plane figures exactly superimpose each other then they are congruent.
- SSS Congruence of two triangles: Two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.
- SAS Congruence of two triangles: Two triangles are congruent if two sides and the angle included between these sides in one of the triangles are equal to the corresponding sides and the angle included between these sides of the other triangle.
- ASA Congruence of two triangles: Two triangles are congruent if two angles and the side included between these angles in one of the triangles are equal to the corresponding angles and the side included between the angles of the other triangle.
- RHS Congruence of two right-angled triangles: Two right angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.
- AAA Congruence of two triangles don’t exist: Any two triangles with equal angles may not be congruent. They may differ in lengths of their sides.
- Two congruent triangles have same area but any two triangles with same area are not always congruent.
- In an isosceles triangle, angles opposite to equal sides are always equal.
- The bisector of vertical angle of an isosceles triangle is perpendicular to its base.
