Question

if two alltitudes of a triangle are equal,prove that it is an isosceles triangles.​

Answer 1

We are given a triangle and two equal altitudes. Let us take the following.

ABC with BD == CE (equal altitudes).

Now we will prove two triangles congruent.

Let us consider BEG and CDB.

BD == CE (given)

BC == BC (common)

L_BEC == L_CDB (each 90°)

Hence, BEG = CDB (RHS rule)

- EBC = DCB(corresponding parts of congruent triangles)

Using this, ⇒ AB == AC (sides opposite to equal angles are equal) Since two sides are equal, the triangle is an isosceles triangle. If 2 altitudes of a triangle are equal then the triangle formed is an isosceles triangle. Note: 1) The students can also use other methods to prove that the triangle is an isosceles triangle. For example

Consider 6 ABD and 6 ACE. BD = CE (given) LEDA= LCEA (each 90°) LEAD= LCAE(common) Hence,6 ABD rv 6 ACE (ASA rule) ⇒ AB = AC (corresponding parts of congruent triangles) Since the two sides of a triangle are equal, the triangle is an isosceles triangle.

2) While selecting a pair of triangles to prove the sides equal, it should be kept in mind that the triangles include the required side. 3) The RHS rule involves a right angle, hypotenuse and any one side. ASA rule involves any one side and two corresponding angles.

Answer 2

Answer:

Since two sides are equal, the triangle is an isosceles triangle. If 2 altitudes of a triangle are equal then the triangle formed is an isosceles triangle. Consider △ABD and △ACE. Since the two sides of a triangle are equal, the triangle is an isosceles triangle.