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As shown in the figure, in the quadrilateral ABCD, AC = BD, m and N are the midpoint of AB and CD respectively, Mn intersects BD and AC at points E and f respectively, and G is the intersection of diagonal AC and BD. are Ge and GF equal? Why?
Take the midpoint o of BC and connect Mo, no,
Then Mo parallel equals AC / 2, no parallel equals BD / 2,
So Mo = no,
Therefore, AFM = omn = Onm = den,
So Ge = GF
As shown in the figure, in the quadrilateral ABCD, angle a plus angle B is equal to 90 degrees, m and N are the midpoint of AB and CD respectively, AB is parallel to CD, and Mn is equal to half AB minus CD
Extend AC and BD to point O, connect on and OM, and OM to point P
Angle a plus angle B is equal to 90 degrees → ∠ o = 90,
In the right angle △ OCD, n is the midpoint of CD → on = CN = nd = CD / 2
In the right angle △ OAB, M is the midpoint of ab → om = am = MB = AB / 2
Because AB is parallel to CD, → CP / am = op / OM = Pd / MB → CP = PD → P is the midpoint of CD → P and N coincide → o, N and m are on the same straight line → Mn = om-on = (AB / 2) - (CD / 2) = (ab-cd) / 2
As shown in the figure, it is known that the length of each side and diagonal of the space quadrilateral ABCD is equal to a, and points m and N are the midpoint of AB and CD respectively
Finding the cosine of the angle between an and cm
This space quadrilateral is a regular tetrahedron after connecting diagonal lines
Make a parallel line of an through point m, cross BN to point P, and connect PC
The angle between an and cm is the complement of angle MCP
Let the side length be equal to 2, then MP = (√ 3) / 2 is calculated
MC=√3
PC=(√7)/2
cosMCP=2/3
So the cosine of the angle is - 2 / 3
The edges and diagonals of the space quadrilateral ABCD are equal, and the points m and N are the midpoint of AB and CD respectively. Find the length of Mn
Let the side length be 2, then an = radical 3. Mn = radical 2
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