Question

give one example for rhs rule

Answer 1

RHS rule Congruence of right angled triangleillustrates that, if hypotenuse and one side of right angled triangle are equal to the corresponding hypotenuse and one side of another right angled triangle; then both the right angled triangle are said to be congruent. 

Example: Following are two diagrams of triangle with few of its measurements: 


Is △ ABC ≅ △ PQR 

Solution: As shown in the given diagrams: 

△ ABC is a right angled triangle at ∠ B 
△ PQR is a right angled triangle at ∠ Q 

Also, we have: 
∠ B = ∠ Q (90° each) 
BC = QR (3 cm) 
AC = PR (6 cm) 

Therefore, RHS congruence rules apply here and we get the following corresponding relationships: 

A ↔ P 
B ↔ Q 
C ↔ R 

Hence, △ ABC ≅ △ PQR 

Justification / Proof - RHS Congruence Rule

Now, lets justify or proof of RHS Rule of Congruence with the help of following three checks: 

Check 1: 
There is a given right angled triangle XYZ right angled at X and length of one side XY is 5cm. You are asked to construct a triangle ABC (right angled at B) congruent to triangle XYZ. 
Can you do that ?? 
With length of one side is given i.e. 5cm, following right angled triangles can be formed: 

From the above diagram of triangles, you can observe that given triangle XYZ can be any of the following, or in other words we can say that we are not sure which diagram of triangle ABC is congruent to Triangle XYZ. 

Hence, this confirms that two triangles cannot be congruent, if one side of a right angled triangle is equal to the corresponding one side of another right angled triangle. 

Check 2: 
There is a given right angled triangle XYZ right angled at X and length of hypotenuse YZ is 7 cm. You are asked to construct a triangle ABC (right angled at B) congruent to triangle XYZ. 
Can you do that ?? 
With length of hypotenuse is given i.e. 7 cm, following right angled triangles can be formed: 

From the above diagram of triangles, you can observe that given triangle XYZ can be any of the following, or in other words we can say that we are not sure which diagram of triangle ABC is congruent to Triangle XYZ. 

Hence, this confirms that two triangles cannot be congruent, if hypotenuse of a right angled triangle is equal to the corresponding hypotenuse of another right angled triangle. 

Answer 2

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