Hello!

It is well-known that in any parallelogram the opposite angles are equal. A rhombus is a parallelogram, so the angles `ABC` and `ADC` are congruent.

Also, it is known that any diagonal of a rhombus bisects the corresponding angles. Therefore angles `ADN` and `CDN` are congruent, and `ABM` and `CBM` are congruent. From this and the first paragraph we infer that the angles `CDN` and `CBM` are congruent (both are halves of the congruent angles).

Now we can finish the proof. The triangles `DNC` and `BMC` have two pairs of congruent sides: ` ``DN = BM` by the conditions and `DC = BC` by definition of rhombus. Also the angles between these sides are equal in both triangles, `CDN = CBM` as proved above. Therefore these triangles are congruent by the side-angle-side rule (SAS).

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now