ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Then:
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Answered by
5
Answer :
ABC is an isosceles triangle in which altitudes BE & CF are drawn
to sides Ac and AB respectively . Show that these altitudes are equal
Step-by-step explanation :
ΔABC is an isosceles triangle
∴ AB = AC
BE = CF
⇒ ∠ACB = ∠ABC { Angles opposite to equal sides are equal }
In ΔBEC and ΔCFB , we have
- ∠EBC = ∠FCB { Proved }
- BC = CB { Common }
- ∠BEC = ∠CFB { Each 90° }
Therefore , ΔBEC ≌ ΔCFB → { by using ASA criterian }
BE = CF { CPCT }
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Answered by
12
Answer:
- BE = CF ( By C P C T )
Step-by-step explanation:
★ GIVEN :
- ΔABC is an isosceles triangle
★ TO PROVE :
- BE = CF
★ SOLUTION :
- We need to about RHS Congruency to answer these.
- In ∆ ABC AND AC
➨∠ AEB = ∠ AFC ( 90° )
➨ ∠ BAE = ∠ CAF ( Common )
➨ and BE = CF
➨ By ∆ AS
➨ ∆ ABE = ∆ ACF
➨ AB = AC
★ FINAL ANSWER :
- BE = CF ( By C P C T )
∴ Hence, ∆ ABC is isosceles triangle.
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