Isosceles Triangle: Calculate ∠BAD Using Height Properties

Question

ABC isosceles triangle (AB=AC).

Given AD height.

Find the size of the angle $∢\text{BAD}$ .

Video Solution

Solution Steps

00:00 Determine angle BAD

00:03 The following is an isosceles triangle and a perpendicular according to the given data

00:11 The perpendicular in an isosceles triangle is also a median

00:18 The perpendicular in an isosceles triangle is also an angle bisector

00:25 Angle BAD equals half of angle A

00:32 Substitute in the appropriate value according to the given and solve for angle BAD

00:37 This is the solution

Step-by-Step Solution

In $\triangle ABC$ , since $AB = AC$ , the triangle is isosceles, and the base angles $\angle ABC$ and $\angle ACB$ are equal. Given that $\angle BAC = 70^{\circ}$ , the sum of the angles in a triangle is $180^{\circ}$ .
Therefore, the two base angles together are $180^{\circ} - 70^{\circ} = 110^{\circ}$ .
Since these angles are equal, each is $\frac{110^{\circ}}{2} = 55^{\circ}$ .

Since $AD$ is the height from $A$ to $BC$ , it bisects $\angle BAC$ .
Thus, $\angle BAD = \frac{\angle BAC}{2} = \frac{70^{\circ}}{2} = 35^{\circ}$ .

Therefore, the size of $\angle BAD$ is $\textbf{35 degrees}$ .

Answer

Related Subjects

The Sum of the Interior Angles of a Triangle The sides or edges of a triangle Triangle Height Exterior angles of a triangle Median in a triangle Center of a Triangle - The Centroid - The Intersection Point of Medians All terms in triangle calculation