Question

If the bisector of vertical angle of a triangle is perpendicular to the base of triangle is

(a) an Equilateral triangle

(b) a scalene triangle

(c) an obtuse angled triangle

(d) an acute angled triangle.​

Answer 1

Answer:

isosceles

Step-by-step explanation:

If the bisector of the vertical angle of a triangle bisects the base, show that the triangle is isosceles.

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Answer 2

If the bisector of the vertical angle of a triangle is perpendicular to the base of the triangle, then the triangle is an isosceles triangle.

Step-by-step explanation:

• Let us consider a triangle ABC in which AD is the bisector of ∠A meeting BC in D such that BD=CD
• With reference to the image, AD is produced to E such that AD=DE and connect EC.
• In ΔADB and ΔEDC, we have AD=DE

                         ∠ADB = ∠CDE (∵ Vertically opposite angles are equal)

• By using the SAS criterion of congruence,

                          ΔADB ≅ ΔEDC

                       ⇒ AB = EC ------- ($1$)

                       ⇒ ∠BAD = ∠CAD

                       ⇒ ∠CAD = ∠CED

• Therefore, AC = EC and AC = AB

• In an isosceles triangle, at least two sides of the triangle are equal and we have AB = AC
• Hence ΔABC  is an isosceles triangle.