Question

state and explain the RHS property in congruence of triangles​

Answer 1

RHS Congruence Rule

Theorem: In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.

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Answer 2

Answer:

RHS Congruence Rule

Theorem:  In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.

Explanation:

Solved Example

Question: In the following figure, AB = BC and AD = CD. Show that BD bisects AC at right angles.

Congruence Of Triangles

Solution: We are required to prove ∠BEA = ∠BEC = 90° and AE = EC.

Consider ∆ABD and ∆CBD,

AB = BC                                                 (Given)

AD = CD                                                (Given)

BD = BD                                                (Common)

Therefore, ∆ABD ≅ ∆CBD                 (By SSS congruency)

∠ABD = ∠CBD                                     (By CPCT)

Now, consider ∆ABE and ∆CBE,

AB = BC                                                (Given)

∠ABD = ∠CBD                                     (Proved above)

BE = BE                                                (Common)

Therefore, ∆ABE≅ ∆CBE                  (By SAS congruency)

∠BEA = ∠BEC                                     (CPCTC)

And ∠BEA +∠BEC = 180°                 (Linear pair)

2∠BEA = 180°                                    (∠BEA = ∠BEC)

∠BEA = 180°/2 = 90° = ∠BEC

AE = EC                                                (CPCTC)

Hence, BD is a perpendicular bisector of AC.