Question

If the altitude from the one vertex of a triangle bisect the opposite side prove that triangle is isoceles.

Answer 1

Answer:

Hello. Find your answer in the attachment. Hope it will help

Answer 2

It is proved below If the altitude from the one vertex of a triangle bisects the opposite side proves that the triangle is isosceles.

Given: Altitude from the one vertex of a triangle bisects the opposite side.

To prove: The triangle is isosceles.

Construction: Draw a figure with the help of the given information. The figure is in the attachment.

Proof:

Let Altitude AD from the one vertex A of a triangle ABC bisect the opposite side BC.

In ΔABD & ΔACD

∠ADB = ∠ADC ( Each = 90°)

BD = CD            (Given- Altitude AD bisect the opposite side BC)

AD = AD             (Common)

ΔABD ≅ ΔACD  (by SAS congruency Criteria)

AB = AC (corresponding parts of Congruent Triangles are always equal in short CPCT)

Therefore ∆ABC is an isosceles triangle.

Hence, it is proved that If the altitude from the one vertex of a triangle bisects the opposite side proves that the triangle is isosceles.

Learn more on Brainly:

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i) ABE ≅ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

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Prove that the medians bisecting the equal sides of an isosceles triangle are also equal ?

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