Question

cde is an equilateral triangle formed on a side cd of a square abcd.show that ∆ADE=∆BCE.

Answer 1

Hope it helps ya.....
Cheers

Answer 2

Answer:

The triangles are congruent by SAS rule.

Step-by-step explanation:

Given CDE is an equilateral triangle formed on a side CD of a square ABCD.

We have to prove that ∆ADE≅∆BCE.

Since all sides of equilateral triangle are equal and all angles are of 60°

⇒ CD=DE=EC  → (1)

Since all sides of square are congruent and all angles are of 90°

⇒ AB=BC=CD=DA  → (2)

∴ ∠ADE=∠ADC+∠CDE=90+60=150°

∠BCE=∠BCD+∠DCE=90+60=150°

In ∆ADE and ∆BCE

AD=BC    (∵ From 2)

DE=EC     (∵ From 1)

∠ADE=∠BCE    (∵each 150°)

By SAS congruency rule ∆ADE≅∆BCE.