Question

in the adjoining figure triangle ABC is an isosceles triangle in which AB=AC . If E and F be the midpoint of AC and AB. prove that BE=CFthe adjoining

Answer 1

Hlo mate :-

Solution :-

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Given:-
AB = AC

Also , BD and CE are two medians


Hence ,
E is the midpoint of AB and
D is the midpoint of CE

Hence ,

1/2 AB = 1/2AC
BE = CD

In Δ BEC and ΔCDB ,

BE = CD [ Given ]
∠EBC = ∠DCB [ Angles opposite to equal sides AB and AC ]
BC = CB [ Common ]

Hence ,

Δ BEC ≅ ΔCDB [ SAS ]


BD = CE [ cpct ] Proved

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Answer 2

HEY MATE HERE IS YOUR ANSWER

$\rule {168} {2}$

$\underline \bold {Thanks \: for\: Question}$

$\rule {168} {2}$

Solution :-

Given :-

✔️ AB = AC

✅ BD and CE are two medians

✅ E is the mid point of AC

✔️ D is the mid point of AB

$\huge {Therefore,}$

$\huge = > \frac{1}{2} ab = \frac{1}{2} \: ac$

➡️ BE = CD

In ⛛ BEC and ⛛ CBD,

➡️ BE = CD [GIVEN]

➡️ BC = CB [COMMON]

➡️ /_ECB = /_DCB [ Angle opposite to equal sides]

Therefore,

⛛ BEC = ~ ⛛ CBD [ By SAS congruence]

Therefore,

➡️ $\huge {BE = CF [CPCT]}$

$\huge \boxed {HENCE, PROVED}$

$\rule {168} {2}$

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Ansh as ans81