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.
"
Given:
ΔABC and ΔADC are two equilateral triangles on a common base AC.
To do:
We have to show that it is a Rhombus.
Solution:
In triangle ABC,
AB = AC = BC and
In triangle ADC,
AD = AC = DC
Each angle of an equilateral triangle is equal to 60°.
Therefore,
$\angle A= 60°+60 °=120°$
$\angle B=60°$
$\angle C=60°+60° =120°$ and
$\angle D=60°$
Also,
$AB=BC=CD=AD$
We know that,
In a rhombus all the sides are equal.
Therefore,
ABCD is a rhombus.
Hence proved.
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