Question

Show that these altitudes are equal.
Na2O GA
B
NAO
ch
4.
ABC is a triangle in which altitudes BD and CE to sides AC
and AB are equal (see figure). Show that
(1) AABD = AACE
(1) AB = AC i.e., ABC
is an isosceles triangle.​

Answer 1

Answer:

In right-angle triangles BCE and CBF, we have,

BC = BC (common hypotenuse);

BE = CF (given).

Hence BCF and CBF are congruent, by RHS theorem. Comparing the triangles, we get ∠B=∠C.

This implies that

AC = AB (sides opposite to equal angles).

Similarly,

AD=BE⇒∠B=∠A

⇒AC=BC

Together, we get AB=BC=ACor △ABC is equilateral. [henceproved]

solution

Answer 2

Step-by-step explanation:

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