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Step-by-step explanation:
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sameersinhaa04
sameersinhaa04
18.03.2018
Math
Secondary School
+5 pts
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Cde is an equilateral triangle formed on a side cd of a square abcd.show that ∆ADE=∆BCE.
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eminemrules101
To prove congruence or similarity?
eminemrules101
eminemrules101
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SerenaBochenek
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.