in the adjacent figure AC=AE, AB=AD,angleBAD=angleEAC . Show that BC=DE
Answers
Answer:
Answer:
Congruence of triangles:
Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.
In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.
It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.
Criteria for congruence of triangles:
There are 4 criteria for congruence of triangles.
SAS( side angle side):
Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.
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Solution:
First show that ΔABC ≅ ΔADE by using SAS rule and then use CPCT to show given result.
Given,
AC = AE, AB = AD and ∠BAD = ∠EAC
To prove:
BC = DE
Proof: We have
∠BAD = ∠EAC
(Adding ∠DAC to both sides)
∠BAD + ∠DAC = ∠EAC + ∠DAC
⇒ ∠BAC = ∠EAD
In ΔABC and ΔADE,
AC = AE (Given)
∠BAC = ∠EAD (proved above)
AB = AD (Given)
Hence, ΔABC ≅ ΔADE (by SAS congruence rule)
Then,
BC = DE ( by CPCT.)
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Step-by-step explanation: