If the altitude from two vertices of a triangle to the opposite sides are equal, then the triangle will be:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. isosceles triangle.
Two altitudes BE and CD are equal.
In ΔABE and ΔACD,
BE = CD
∠BEA = ∠CDA = 90°
∠BAE = ∠CAD (Common Angle)
∠ABE = ∠ACD (Angle sum property)
So, ΔABE is similar to ΔACD
Then, AB = AC
When two sides of a triangle are equal, then it is isosceles.
Therefore, if the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is isosceles.