ABCD is a rectangle ∠ EDC = ∠ cab ∠ Dec = 90 ° (1) verification: AC ‖ de (2) through B as BF ⊥ AC connected to f to judge the shape of becf and explain the reason
(1)∵∠EDC=∠CAB=∠ACD
∴AC∥DE
(2)∵∠FAB=∠EDC ∠DEC=90° BF⊥AF AB=DC
∴△ABF≌△DCE
Ψ BF = CE ∠ ABF = ∠ DCF and ab ‖ DC
∴BF∥CE
The BCEF is a parallelogram
RELATED INFORMATIONS
- 1. The quadrilateral ABCD is a rectangle,
- 2. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) verification: AC ‖ de( 2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, please explain the reason (do not judge parallelogram)
- 3. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) Verification: AC ‖ de; (2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, and explain the reason
- 4. As shown in the figure, in rectangle ABCD, AE = BF = 3, EF ⊥ ed intersects BC at point F, and the circumference of rectangle is 22. Calculate the length of EF
- 5. It is known that the circumference of rectangle ABCD is 18, e and F are the points on the edges AB and BC respectively, and AE = BF = 1. If EF is perpendicular to BD, the area of this rectangle can be calculated
- 6. As shown in the figure, ▱ ABCD, if EF crosses the intersection of diagonal lines o, ab = 4, ad = 3, of = 1.3, then the perimeter of quadrilateral BCEF is______ .
- 7. In the parallelogram ABCD, if EF passes through the intersection of diagonals o, ab = 4, ad = 3, the perimeter of quadrilateral BCEF = 9.6, the length of of of can be obtained
- 8. If AB = 5, BC = 7, OE = 2, then the perimeter of EFDC is () A.14 B.15 C.16 D.18
- 9. If the parallelogram ABCD and EF cross the focus o, ab = 3, BC = 5 and OE = 2 of the diagonal, what is the perimeter of the parallelogram ADFE
- 10. Given that the side length of square ABCD is 2 and point P is a point on diagonal AC, the maximum value of (. AP +. BD) ·(. Pb +. PD) is______
- 11. 1. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) prove: AC ‖ de; (2) make BF ⊥ AC at point F through point B, connect
- 12. As shown in the figure, in square ABCD, the diagonal lines AC and BD intersect at point O, and the points EF are on AC and BD respectively, and BF = CE connects be, AF.AF There is a relation between be and quantity
- 13. As shown in the figure, the diagonal lines AC and BD of rectangular ABCD intersect at point O, EF ⊥ BD at point O, ad at point E, BC at point F, and EF = BF
- 14. Parallelogram ABCD parallelogram abef is on the same side AB, m, n are on the diagonal AC, BF respectively, and am: AC = FN: FB to prove Mn / / plane ADF
- 15. ABCD and abef are parallelograms, m and N are the points on diagonal AC and BF respectively, and am: FN = AC: BF
- 16. As shown in the figure, let ABCD and abef be parallelograms, they are not in the same plane, m and N are the points on the diagonal AC and BF respectively, and am: FN = AC: BF (Continued), prove: Mn ‖ plane bec
- 17. It is known that ABCD and abef are two squares and not in the same plane, m and N are the points on the diagonal AC and FB respectively, and am = FN It is suggested that the extension line connecting an and be should be connected to g
- 18. As shown in the figure, the planes of two congruent squares ABCD and abef intersect AB, m ∈ AC, n ∈ FB, and am = FN
- 19. In the parallelogram ABCD, EF is the midpoint of AD and BC respectively The intersection of the center line BD and CE of triangle ABC with O, F and G is the midpoint of OB and OC respectively
- 20. In parallelogram ABCD, de ⊥ AC in E, BF ⊥ AC in F, connect be ` DF, then be ∥ DF? Be = DF? Try to explain your reason