Question

ABC is a triangle in which BE and CF to sides AC and AB are

equal .Show that

a)∆ABE is congruent to∆ACF

b) AB=AC
can i use RHS congruence criteria here?? and full explanation pls​

Answer 1

Hey mate !! Here is your 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.

Given:

ΔABC in which BE perpendicular to AC & CF perpendicular to AB, such that BE=CF.

To Prove:

i) ΔABE ≅ ΔACF

ii) AB=AC

Proof:

(i) Now, Consider two triangles ∆ABE and ∆ACF,

∠A = ∠A (Common)

∠AEB = ∠AFC (each 90°)

BE = CF (Given)

Therefore, ΔABE ≅ ΔACF (by ASA congruence rule)

(ii) Since ΔABE ≅ ΔACF

Thus, AB = AC (by CPCT)

Hope this helps you..

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