ABC and ADC are two equilateral triangles ona commAC (Fig. 11.30). Fin

1.	ABC and ADC are two equilateral triangles ona commAC (Fig. 11.30). Find the angles of theresultingbasequadrilateral. Show that it is a rhombus.
Answer» 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.

ABC and ADC are two equilateral triangles ona commAC (Fig. 11.30). Find the angles of theresultingbasequadrilateral. Show that it is a rhombus.

Answer»

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.