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As shown in the figure, fold the rectangular ABCD paper along EF so that point d coincides with the midpoint d 'of BC side. If BC = 8, CD = 6, CF=______ ．
∵ D ′ is the midpoint of BC, ∵ D ′ C = 12bc = 4; from the properties of folding, we know: DF = D ′ F, let CF = x, then d ′ f = DF = 6-x; in RT △ CFD ', according to Pythagorean theorem, we get: D ′ F2 = CF2 + CD ′ 2, that is: (6-x) 2 = x2 + 42, the solution is x = 53; so CF = 53
In rectangular ABCD, ab = 4cm, BC = 3cm, there is a moving point P moving from point B along BC, CD, BA at the speed of 1cm per second
(1) Find the function relation between area s (square centimeter) and time t (s) of triangle ABP
(2) Draw an image of the function
This is a piecewise function. First, we use the perimeter and the distance to find the bottom or height of Δ. Of course, the final result should be the combination of the area formula and the distance formula
In rectangle ABCD, ab = 3, BC = 4, if the rectangle is folded along the diagonal BD, calculate the shadow area
The shadow area? Refers to finding the overlap of △ abd and △ bc'd after folding. Mark the intersection point ad and e of BC 'after folding. Let AE = X. according to the properties of folding, △ Abe ≌ △ ec'd ≌ be = de ? AB & sup2; + AE & sup2; = be & sup2; ≌ X & sup2; + 3 & sup2; = (4-x) & sup2; get x = 7 / 8 ≌ s shadow = 1 / 2DE * AB = 1 / 2 * (...)
Fold the rectangular ABCD paper along the diagonal BD, and point C falls at the position of point C '
Proving AE = c'e
Let AD and BC 'intersect at point E
Because the rectangular ABCD paper is folded along the diagonal BD, point C falls at the position of point C '
So the triangle BCD is equal to the triangle BC'd
So angle DBC = angle DBC '
Because in rectangle ABCD, AC / / BD
So angle DBC = angle BDA
Because angle DBC = angle DBC '
So angle BDA = angle DBC '
So be = de
Because the triangle BCD is equal to the triangle BC'd
So BC '= BC
Because in rectangle ABCD, ad = BC
So ad = BC '
Because be = de
So ad-de = BC '- be
So AE = c'e
RELATED INFORMATIONS
- 1. If the inner angle of the diamond is 120 ° and the length of its diagonal is 12cm, the perimeter of the diamond is The answer is 48CM or 2 √ 3, remember that there are two cases
- 2. Given that the rectangle ABCD, and ab = 5, ad = 3, establish an appropriate plane rectangular coordinate system, find the coordinates of each vertex of the rectangle
- 3. In the plane rectangular coordinate system, the coordinates of the three vertices of square ABCD are a (0,0), B (- 2,0), D (0,2), then the coordinates of point C are Then the coordinates of the midpoint of the square BC are 2. If point P (a, 3-2a) is on the bisector of the second and fourth quadrants, then the value of a is
- 4. As shown in the figure, two pieces of paper of equal width are crossed and overlapped, and the quadrilateral ABCD of the overlapped part is______ Shape
- 5. As shown in the figure, place a rectangle in the plane rectangular coordinate system, OA = 2, OC = 3, e is the midpoint of AB, and the image of inverse scale function passes through point E and connects with BC Intersection at point F (1) Finding the analytic formula of straight line OB and the analytic formula of inverse scale function (2) Connect of and OE, point P is on the straight line ob, and s triangle AOP = 2S quadrilateral oebf, calculate the coordinates of point P
- 6. What do QA and QC mean?
- 7. It is known that PA is perpendicular to the plane of rectangle ABCD, and M is the midpoint of ab. if PD and ABCD form an angle of 45 degrees, it is proved that plane PCM is perpendicular to plane PCD
- 8. Let the vertex a of the square ABCD be the plane ABCD, PA = AB = a, and find the dihedral angle between the plane PAB and the plane PCD
- 9. In square ABCD, point E.F is on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, what is the area of square ABCD
- 10. As shown in the figure, in the square ABCD, ab = 1, point P is a point on the diagonal AC, and AP and PC are used as the diagonal to make the square respectively, then the sum of the perimeter of the two small squares is______ ．
- 11. If the coordinates of the point a symmetric about the Y axis are (4, - 3), then the coordinates of the point a symmetric about the origin are (4, - 3)
- 12. In the parallelogram ABCD, ab = 5, BC = 3, find the perimeter
- 13. As shown in the figure, the vertex B of square ABCD is the bisector BF of diagonal AC, the point E is the point on BF, and the quadrilateral aefc is a diamond, eh ⊥ AC, and the perpendicular foot is h EH = 1 / 2cf,
- 14. The quadrilateral ABCD is a diamond, the edge AB is on the y-axis, the vertex D is in the first quadrant, B (0, - 4), C (3,0) are known (1) Finding the coordinate of point a (2) Finding the inverse proportion function relation of passing through point d
- 15. Verification: the quadrilateral formed by the parallel lines which cross the vertex of the diamond and make diagonals to the outside of the diamond is a rectangle
- 16. As shown in the figure, in square ABCD, points E and F are on AB and BC respectively, and AE = BF, AF and de intersect at point g. from the given conditions, what conclusions can you draw? Why?
- 17. As shown in the figure, in the quadrilateral ABCD, ab = CD, BF = De, AE ⊥ BD, CF ⊥ BD, e and f respectively. (1) prove: △ Abe ≌ △ CDF; (2) if AC and BD intersect at point O, prove: Ao = Co
- 18. As shown in the figure, in the known parallelogram ABCD, ab = 1 / 2ad, ab = AE = BF, explore the position relationship between EC and FD, and explain the reason
- 19. As shown in the figure, in rectangular ABCD, diagonal lines AC and BD intersect at point O, AE ⊥ at BD and E. if ∠ DAE = 3 ∠ BAE, try to find the degree of ∠ EAC
- 20. In ladder shaped ABCD, the area of triangle ABO is 6 square meters, and the area of triangle ADO is 15. Calculate the area of ladder shaped ABCD. Triangle ABO = triangle doc In ladder ABCD, the area of triangle ABO is 6 square meters, and the area of triangle ADO is 15 square meters. Find the area of ladder ABCD. Triangle ABO = triangle doc