Question

in the given figure AD is the median the angel BAD​

Answer 1

Answer:

The correct option is d.

Step-by-step explanation:

Given information: AD is median, AB=AC, m∠B=35°.

In triangle ABC, two sides of triangle are equal. It means triangle ABC is an isosceles triangle.

$\angle B\cong \angle C$               (Isosceles triangle property)

$m\angle B=m\angle C$               (congruent angle property)

$35^{\circ}=m\angle C$                   (Given, m∠B=35°)

According to angle sum property, the sum of interior angle of a triangle is 180°.

In triangle ABC,

$\angle A+\angle B+\angle C=180^{\circ}$

$\angle A+35^{\circ}+35^{\circ}=180^{\circ}$

$\angle A+70^{\circ}=180^{\circ}$

$\angle A=180^{\circ}-70^{\circ}$

$\angle A=110^{\circ}$

Median of an isosceles triangle divides the triangle in two equal parts.

In triangle ABC, AD is median. So,

$\triangle ABD\cong \triangle ACD$

$\angle BAD\cong \angle CAD$

Angle A is the sum of angle BAD and CAD.

$\angle BAD+\angle CAD=\angle A$

$\angle BAD+\angle BAD=110^{\circ}$            $(\angle BAD\cong \angle CAD)$

$2\angle BAD=110^{\circ}$

Divide both sides by 2.

$\angle BAD=55^{\circ}$

Therefore the correct option is d.

Answer 2

Answer:

d

Step-by-step explanation:

The correct option is d.

Step-by-step explanation:

Given information: AD is median, AB=AC, m∠B=35°.

In triangle ABC, two sides of triangle are equal. It means triangle ABC is an isosceles triangle.

\angle B\cong \angle C∠B≅∠C               (Isosceles triangle property)

m\angle B=m\angle Cm∠B=m∠C               (congruent angle property)

35^{\circ}=m\angle C35∘=m∠C                   (Given, m∠B=35°)

According to angle sum property, the sum of interior angle of a triangle is 180°.

In triangle ABC,

\angle A+\angle B+\angle C=180^{\circ}∠A+∠B+∠C=180∘

\angle A+35^{\circ}+35^{\circ}=180^{\circ}∠A+35∘+35∘=180∘

\angle A+70^{\circ}=180^{\circ}∠A+70∘=180∘

\angle A=180^{\circ}-70^{\circ}∠A=180∘−70∘

\angle A=110^{\circ}∠A=110∘

Median of an isosceles triangle divides the triangle in two equal parts.

In triangle ABC, AD is median. So,

\triangle ABD\cong \triangle ACD△ABD≅△ACD

\angle BAD\cong \angle CAD∠BAD≅∠CAD

Angle A is the sum of angle BAD and CAD.

\angle BAD+\angle CAD=\angle A∠BAD+∠CAD=∠A

\angle BAD+\angle BAD=110^{\circ}∠BAD+∠BAD=110∘ (\angle BAD\cong \angle CAD)(∠BAD≅∠CAD)

2\angle BAD=110^{\circ}2∠BAD=110∘

Divide both sides by 2.

\angle BAD=55^{\circ}∠BAD=55∘

Therefore the correct option is d.