Congruence of Triangles CBSE Class 7 Maths | NCERT Solutions
CONGRUENCE OF TRIANGLES – Online Class 7 Maths
The relationship between two objects that are congruent to each other. Congruence is used for object and their mirror images.
When two objects are superimposed on each other, they are said to be congruent. Their shape and dimensions are the same.
- Line segments with the same
- Angles with the same
Congruence of triangles
What is a triangle?
Triangle refers to the polygon made of three line segments.
Triangles are said to be congruent under the following case
- Same length
- Same height
- Same angles
- Both triangles can be superimposed from side to side.
- Both triangles can be superimposed angle to angle.
In the above figure, ABC and EFD are congruent triangles
Vertices- A and D, B and E and C and F are the same
Sides-AB=ED, AC=DF and BC =FD are same
Angles at BAC=FDE, ABC=FED, and BCA=DFE are same.
Symbol of congruent- ≅
Different rules for congruent triangles
1 SSS ( side-side-side)
When all sides of both triangles are equivalent to the correspondent side. Then SSS rule is applied.
DF=HI, EF=HG, and DE=IG
2 SAS (side-angle-side)
If any two sides and one angle are equivalent to the corresponding two sides and the angles. Then SAS rule is applied.
AB=ED, BC=FE and angle at ABC = angle at FED
3 ASA ( Angle-side-angle)
If any two angles and side included between the angles of one triangle is equivalent to the corresponding two angles and sides of a second triangle. Then ASA rule is applied.
AB=XY, Angle at CAB = angle at YXZ and angle at ABC= angle at ZYX.
4 RHS (Right angle- hypotenuse-side)
If the hypotenuse and a side of a right angle triangle are equivalent to the hypotenuse and aide of a right angle triangle is the same. Then RHS rule is applied.
AC=DF, AB=DE, and angle at ACB= angle at DFE
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