Question

please prove and explain this question​

Answer 1

Step-by-step explanation:

1) AM=BM ( M is midpoint of AB)

CM=DM (given)

angle AMC = angle BMD (V.O.A)

THEREFORE, AMC congruent BMD ( SAS)

2) since, AMC congruent BMD (proved)

therefore, angle MAC = angle MBD (cpct)

THESE ARE ALTERNATE ANGLES

THEREFORE, DB||AC.

Then, angle DBC + angle ACB =180 ( CO-INTERIOR)

angle DBC + 90= 180 ( ABC is right angled at C)

Therefore, angle DBC = 180-90=90.

proved, angle DBC is a right angle.

3) DB=AC (cpct from i)

BC = CB (common)

angle DBC = angle ACB ( =90)

Therefore, DBC congruent ACB ( SAS)

4) Since, DBC congruent ACB (proved)

Therefore DC=AB (cpct)

NOW, 1/2 DC = 1/2 AB

= CM=1/2 AB ( because CM is 1/2 DC)

THAT'S THE ANSWER OF YOUR QUESTION.