Question

ABC and ADC are two equilateral triangles on a common
base AC (Fig. 11.30). Find the angles of the resulting
quadrilateral. Show that it is a rhombus.​

Answer 1

Answer:

Step-by-step explanation:

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.