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

ΔABC and ΔADC are two equilateral triangles on a common base AC.

In triangle ABC, AB = AC = BC and in triangle ADC, AD = AC = DC

From this we get two triangles ABC and ADC are Equilateral Triangles with same side.

The equilateral  triangle have same angle which is equal to 60°

Here AC is the common base, We get a quadrilateral ABCD.  

<A= 60°+60 °=120°, <B=60°, <C=60°+60° =120° and <D=60°

Also AB=BC=CD=AD

All the sides of this quadrilateral are equal , so it is a rhombus.

Answer 2

∆s ABC and ADC are equilateral

AB = BC = CD = AD = AC

and also ∠B = ∠D = 60°

Now, ∠A = ∠BAC + ∠CAD = 60° + 60° = 120°

and ∠C = ∠ACB + ∠ACD = 60° + 60° = 120°

All of its side are equal. Therefore it is a rhombus