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Q: How do you show that from the right angle vertex to the midpoint of the hypotenuse is half the length of the hypotenouse?

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A triangle is not a segment joining a vertex and the midpoint of the side opposite the vertex.

Yes, the median of a triangle is from a vertex to the midpoint of the side opposite the vertex.

It is the line from a vertex of the triangle to the midpoint of the side opposite that vertex.

The length of the circle's diameter

It is the mid point of the angle

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Simply by measuring it. Or by drawing a circle with a radius of half the hypotenuse and having the vertex of the right angle as its centre and if the midpoint of the hypotenuse just touches the circle then this proves it.

A triangle is not a segment joining a vertex and the midpoint of the side opposite the vertex.

Yes, the median of a triangle is from a vertex to the midpoint of the side opposite the vertex.

the median is drawn from the vertex to the midpoint of the opposite side

median

It is the line from a vertex of the triangle to the midpoint of the side opposite that vertex.

The length of the circle's diameter

It is the mid point of the angle

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

A median of a triangle is a line from a vertex of the triangle to the midpoint of the side opposite that vertex.

Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle. The centroid of a triangle is twice as far from a given vertex than it is from the midpoint to which the median from that vertex goes. For example, if a median is drawn from vertex A to midpoint M through centroid C, the length of AC is twice the length of CM. The centroid is 2/3 of the way from a given vertex to the opposite midpoint. The centroid is always on the interior of the triangle.

Assuming that you meant midpoint, it is a median.

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