Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Then:​

Answer 1

Answer:

Yes

BE = CF

You can prove it by AAS

Answer 2

Answer:

Congruence of triangles:

Two A's are congruent if sides and angles

of a triangle are equal to the

corresponding sides and angles of the

other A.

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.

Here we use ASA congruence

ASA(angle side angle):

Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the other triangle. Given:

AABC is an isosceles with AB AC, BE and CF are altitudes. =

To prove:

BE = CF

Proof:

In AAEB and AAFC, ZA = ZA (Common) ZAFC

ZAEB=

(each 90°)

AB = AC (Given)

Therefore, AAEB = AAFC

(by AAS congruence rule)

Thus, BE = CF (by CPCT.) Hence

9 altitudes BE & CF are equal.

Hope this will help you....