Question

 Provide the reasons for the proof. Given: RUMH is a rhombus. RUBM is a rhombus. Prove: RHM = UMB

Answer 1

Here, RUMH and RUBM are two rhombus as shown in the diagram.

As, a rhombus has four equal sides,

so for RUMH, side RH = side HM = side MU = side UR

and for RUBM, side RM = side MB = side BU = side UR

As HM=UR and MB= UR , so we can write HM = MB

Now for two triangles ΔRHM and ΔUMB,

side RH = side MU

side RM = side BU

and side HM = side MB

'Side Side Side' theorem states that if three sides of one triangle are equal to three sides of another triangle respectively, then the two triangles are similar.

That means, ΔRHM = ΔUMB