please give me the correct answer
Answers
GIVEN ;-
- BE = CF ----(1)
BE & CF are altitudes,
- ⟨AEB = ⟨AFC = 90° ----(2)
PROOF ;-
☃️ In ∆ABE & ∆ACF,
- ⟨AEB = ⟨AFC
- ⟨A is a common angle .
- BE = CF
→ AB = AC (CPCT ), i.e. ABC is an isosceles ∆ .
✔️ Hence proved .
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.
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 trian gle.
____________________________________________________________________
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) In ΔABE & ΔACF,
∠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)
Therefore ∆ABC is an isosceles triangle.