Finding Angle ADC in an Isosceles Triangle with Given Median

ABC is an isosceles triangle.

AD is the median.

What is the size of angle ADC ∢\text{ADC} ?

AAABBBCCCDDD

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Step-by-step video solution

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00:00 Determine the size of angle ADC
00:03 AD is a median according to the given information, a median bisects the side
00:06 The triangle is isosceles according to the given information
00:10 In an isosceles triangle, the median is also the height
00:17 The height creates a right angle with the side that it meets
00:23 This is the solution

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1

Understand the problem

ABC is an isosceles triangle.

AD is the median.

What is the size of angle ADC ∢\text{ADC} ?

AAABBBCCCDDD

2

Step-by-step solution

In an isosceles triangle, the median to the base is also the height to the base.

That is, side AD forms a 90° angle with side BC.

That is, two right triangles are created.

Therefore, angle ADC is equal to 90 degrees.

3

Final Answer

90

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