ABC is an isosceles triangle.
AD is the median.
What is the size of angle ?
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ABC is an isosceles triangle.
AD is the median.
What is the size of angle ?
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.
90
Is the straight line in the figure the height of the triangle?
In an isosceles triangle, two sides are equal in length. The median from the vertex angle to the base creates two congruent right triangles, making the median perpendicular to the base by symmetry.
A median connects a vertex to the midpoint of the opposite side. An altitude is perpendicular to the opposite side. In isosceles triangles, the median to the base is also the altitude!
This special property only works for isosceles triangles. In other triangles, the median and altitude to the base are different lines and don't create 90° angles.
Think "isosceles = symmetry". The equal sides create perfect symmetry, so the median splits everything evenly and perpendicularly. Draw it out and you'll see the two identical right triangles!
The orientation doesn't matter! Whether the triangle points up, down, or sideways, the median to the base in any isosceles triangle will always be perpendicular, creating a angle.
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