Question

ABC and ADC are two equilateral triangles on a common base AC. Find the angles of the resulting
quadrilateral. Show that it is a rhombus.​

Answer 1

Answer:

Answer

△ABCand△ADCaretwoequilateraltrianglesonacommonbaseAC.

Sinceallthesidesofequilateraltrianglesareequal

⟹AB=BC=AC=AD

Nowin△ABC

∠BAC=∠ACB=∠ABC(Equilateraltrianglehasallanglesequal)

⟹∠BAC=∠ACB=∠ABC=60...(1)

Nowin△ADC

∠ADC=∠DCA=∠CAD=60....(2)

In□ABCD

∠BAD=∠BAC+∠CAD

⟹∠BAD=60+60=120[From(1)and(2)]

Also,∠BCD=∠BCA+∠ACD

⟹∠BCD=60+60=120[From(1)and(2)]

Also∠ABC=∠ADC=60

Since∠BAD=∠BCDand∠ABC=∠ADCandAB=BC=AD=CD

Hencethequadilateralisarhombus

Answer 2

Answer:

yes it is correct answer