Question

BD and CF are equal attitude of a triangle ABC using RHS congruence rule prove that triangle ABC is isosceles​

Answer 1

Answer:

Let's draw the figure ( I used ms paint for the figure).

GIVEN:

• BD=CF
• Since BD and CF are altitudes, ∠CDB=90°, ∠BFC=90°. Thus, ΔBDC and ΔCFB are right-angled triangles.

RTP:

∠B=∠C (We just have to prove ∠B=∠C because Isosceles triangles have equal base angles)

PROOF:

RHS congruence rule stated that in two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.

If you look at the figure properly, ΔBDC and ΔCFB are right-angled triangles.

• BD = CF [GIVEN]
• BC = BC [COMMON]

Thus, by RHS congruency, ΔBDC≅ΔCFB.

By CPCT, ∠B=∠C.

Base angles of this triangle are equal. Thus, ΔABC is isosceles.

HOPE THIS HELPS :D

Answer 2

Answer:

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