How to prove that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse with the theorem of rectangle property How to prove that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse with the theorem of rectangle property

One of the properties of rectangles is that diagonals are equal
Draw a rectangle and then draw two diagonals. You can see that the two diagonals are equal in length and bisect each other
If we make two adjacent sides and one diagonal line of a rectangle into a right triangle, we can see that the other diagonal is the middle line of the shoe edge of the right triangle. Its length is half of the length of the hypotenuse

What is the name of the theorem that the median line of the hypotenuse of a right triangle is half of the hypotenuse?

Theorem of the central line of the hypotenuse of a right triangle: if a triangle is a right triangle, the center line on the hypotenuse of the triangle is equal to half of the hypotenuse

Proof: the center line on the hypotenuse of a right triangle is equal to half of the hypotenuse

It is known that: as shown in the figure, in △ ABC, ∠ ACB = 90 ° and CD is the center line on the hypotenuse AB, proving that CD = 12ab; it is proved that, as shown in the figure, extend CD to e so that de = CD, connect AE and be, ∵ CD is the central line on the hypotenuse AB,

Is the inverse proposition that the center line on the hypotenuse of a right triangle equals half of the hypotenuse? I am the second phase of the curriculum reform in Shanghai, if established in which book?

establish
Original proposition 1: if a triangle is a right triangle, then the center line of its hypotenuse is equal to half of the hypotenuse
Inverse proposition 1: if the center line of one side of a triangle is equal to half of the side, then the triangle is a right triangle and the side is the hypotenuse of the right triangle
The inverse proposition 1 is correct. If the midpoint of the edge is taken as the center of the circle, and the length of the middle line is the radius of the circle, then the side becomes the diameter of the circle. The other vertex of the triangle is on the circle, and the vertex angle is the circumference angle of the circle. Because the circular angle on the diameter is a right angle, the inverse proposition 1 holds
Original proposition 2: if BD is the central line on the hypotenuse AC of the right triangle ABC, then it is equal to half of AC
Inverse Proposition 2: if one end B of segment BD is the vertex of right triangle ABC, the other end D is on hypotenuse AC, and BD is half of AC, then BD is the center line of hypotenuse AC
If the length of the three sides of a right triangle is ab = 3, BC = 4, AC = 5. The half length of the hypotenuse is 2.5, and the height of the hypotenuse is be = (3 * 4) / 5 = 2.4, a point d must be found on the segment AE so that BD = 2.5, but BD is not the center line of AC side, because the midpoint of AC side is on the line EC

The inverse proposition of this proposition is that the central line on the hypotenuse of a right triangle is equal to half of the hypotenuse______ .

The inverse proposition of theorem "the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse": if the center line on one side of a triangle is equal to half of this side, then the triangle is a right triangle

What is the inverse proposition of the proposition that the central line on the hypotenuse of a right triangle is equal to half of the hypotenuse? Is it true? RT I want to ask whether its converse is true. Can it be regarded as a theorem?

He is a true proposition
Inverse proposition: if the center line on one side of a triangle is equal to half of the side, then the triangle is between triangles

The inverse proposition of this proposition is that the central line on the hypotenuse of a right triangle is equal to half of the hypotenuse______ .

Proof: the center line on the hypotenuse of a right triangle is equal to half of the hypotenuse

In the right triangle ABC, the angle c is equal to 90 degrees, the angle B is equal to 30 degrees, the point D is a point on BC, and AC is equal to CD, and ad is equal to 10 Steps to solve the problem Thank you very much

In the right triangle ABC, angle c equals 90 degrees and angle B equals 30 degrees
AC = CD, so △ ACD is an isosceles right triangle,
AC = 5 root number 2
AB = 2 * AC = 10 root number 2
AB square = 200

As shown in the figure, in RT △ ABC, ∠ C = 90 °, a = 30 °, BD bisection ∠ ABC, CD = 1cm, find the length of ab

∵ in RT △ ABC, ∵ C = 90 °, a = 30 °,
∴AB=2BC，∠ABC=60°．
And ∵ BD ∵ ABC,
∴∠CBD=30°，
∴BC=DC•cot30°=
3cm，
∴AB=2
3cm．

How to prove that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse with the theorem of rectangle property How to prove that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse with the theorem of rectangle property