Question

5. Construct a quadrilateral RACE in which
RA = 5.5 cm, angle RAC = 110°, AC = 5 cm,
angle ACE = 80°, and angle ARE = 60°.​

Answer 1

Step-by-step explanation:

Given: A quadrilateral ABCD, in which BM ⊥ AC and DN ⊥ AC and BM = DN.

To prove: AC bisects BD; or DO = BO

Proof:

Let AC and BD intersect at O.

Now, in ∆OND and ∆OMB, we have:

∠OND = ∠OMB (90o each)

∠DON = ∠ BOM (Vertically opposite angles)

Also, DN = BM (Given)

i.e., ∆OND ≅ ∆OMB (AAS congurence rule)

∴ OD = OB (CPCT)

Hence, AC bisects BD.