1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In the given figure, △ABC is an isosceles triangle in which AB=AC . If AB and AC are produced to D and E respectively such that BD=CE.Is BE=CD ?

A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A TrueGiven:(1) ΔABC is an isosceles triangle.⟹ AB=AC.(2) BC=CE. Since AB=AC,∴∠ABC=∠ACB [Since angles opposite to equal sides of a triangle are equal]∴180o−∠ABC=180o−∠ACB∠DBC=∠ECB ………..(1)[ since ABD and ACE are straight lines].In triangles DBC and ECB,∠DBC=∠ECB (from (1))BD=CE (given)BC=BC (common side)∴ΔDBC∼ΔECB [by SAS criteria].So ,since triangles are congruent,∴DC=EB.Hence, BE=CD is true.Therefore, the statement is true.Hence, option A is correct.

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program