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In the trapezoidal ABCD, ab = CD, e is the midpoint of AD
AB = CD, isosceles trapezoid, angle a = angle D, e is the midpoint of AD, AE = De, triangle Abe and triangle DCE are congruent, EB = EC
In the trapezoidal ABCD, ab ‖ CD, ∠ a = 90 °, ab = 2, BC = 3, CD = 1, e is the midpoint of AD, and ∠ BEC = 90 ° is proved
Certification:
Extend CE and cross the extension line of BA at point F
∵AB‖CD
∴∠DCF=∠F,∠D=∠FAE
∵AE=DE
∴△AEF≌△CED
∴EF=CE,AF=CD=1
∴BF=2+1=3
∴BF=BC
∵EF=EC
∴BE⊥CF
That is, BEC = 90 degree
As shown in the figure, in trapezoidal ABCD, ∠ d = 90 ° and M is the midpoint of ab. if cm = 6.5 and BC + CD + Da = 17, the area of trapezoidal ABCD is ()
A. 20B. 30C. 40D. 50
Extend the intersection point of CM and DA at E. ∵ ad ∥ BC, ∵ Mae = ∥ B, ∥ e = ∥ BCM. Am = BM, ≌ ame ≌ BMC. ∥ me = MC = 6.5, AE = BC. BC + CD + Da = 17, ∥ d = 90 °, de + DC = 17 ①, de2 + DC2 = CE2 = 169 ②. ∥ de · CD = 12 [(de + DC) 2-de2-dc2] = 60. ∥ the area of trapezoidal ABCD is 12de · CD = 30
RELATED INFORMATIONS
- 1. As shown in the figure, in trapezoidal ABCD, ∠ d = 90 ° and M is the midpoint of ab. if cm = 6.5 and BC + CD + Da = 17, the area of trapezoidal ABCD is () A. 20B. 30C. 40D. 50
- 2. In trapezoidal ABCD, ad ∥ BC, ab = 4, BC = 9, CD = 5, Da = 6. (1) prove ab ⊥ BC; (2) find the area of trapezoidal ABCD
- 3. In trapezoidal ABCD, AD / / BC, ∠ ABC = 60 °, DCB = 30 °, ab = 4, BC-AD is calculated
- 4. There is a little E in the quadrilateral ABCD,
- 5. As shown in the figure, in ▱ ABCD, the diagonal AC = 21cm, be ⊥ AC, the perpendicular foot is e, and be = 5cm, ad = 7cm, then the distance between AD and BC is______ cm．
- 6. It is known that the perimeter of the parallelogram ABCD is 50cm, the diagonals intersect at point O, the perimeter of △ AOB is 5cm longer than that of △ BOC, and the lengths of AB and BC are calculated No picture
- 7. Known: as shown in the figure, the quadrilateral ABCD is a parallelogram, e and F are two points on the straight line BD, and de = BF. (1) prove: AE = CF; (2) connect AF and CE, then is the quadrilateral afce a parallelogram?
- 8. The diagonals AC and BD of parallelogram ABCD intersect at O, e and F, which are two points on DB, and de = BF I'm sorry to trouble you to copy it,
- 9. If the perimeter of parallelogram is 48mm and the diagonal intersects o, the perimeter of triangle AOB is 4mm longer than that of triangle BOC, then the lengths of AB and BC are equal to?
- 10. It is known that the perimeter of a parallelogram is 20 cm. A diagonal divides it into two triangles with a perimeter of 16 cm. How many cm is the diagonal?
- 11. As shown in the figure, in trapezoidal ABCD, ad is parallel to BC, AF is vertical, BC and points F, m are the midpoint of CD, angle B is 45 degrees, AF is 4, EF is 7 Find ABCD area
- 12. It is known that in trapezoidal ABCD, ad is parallel to BC, AB is parallel to de, AF is parallel to DC, e and F are on edge BC As shown in the figure, in the trapezoidal ABCD, ad ‖ BC, ab ‖ De, AF ‖ DC, e and F are on the side BC, and the quadrilateral aefd is a parallelogram (1) What is the equivalent relationship between AD and BC (2) When AB = DC, it is proved that the quadrilateral aefd is a rectangle I want to prove that the process is not an equation
- 13. As shown in the figure, in the square ABCD, point P is a point on the diagonal AC, PE ⊥ AB, PF ⊥ BC, and the perpendicular feet are points E and f respectively. If the perimeter of the square ABCD is 8cm, then the perimeter of the quadrilateral EBFP is______ cm．
- 14. In the isosceles triangle ABCD, ab = AC, ∠ a = 36 ° and BD is the square of ∠ ABC, then calculate AD / AC
- 15. The quadrilateral ABCD is the inner boundary quadrilateral of the circle, the diagonal AC and BD intersect at e, the extended DA and CB intersect at F, the angle CAD = 60 degrees, DC = De, it is proved that a is the outer center of the triangle bef How does angle F + angle AEB equal to 60 degrees?
- 16. It is known that as shown in the figure, ad and BC intersect at point O, ∠ cab = ∠ DBA, AC = BD
- 17. As shown in Figure 1, in quadrilateral ABCD, ad ∥ BC, de bisects ∥ ADB, ∥ BDC = ∥ BCD, (1) (2) if the bisector of abd and the extension of CD intersect at f (Fig. 2), and F = 55 °, find ABC
- 18. As shown in the figure, in the quadrilateral ABCD, the diagonal AC and BD intersect at point E, and ∠ cab = ∠ CBD. Given AB = 4, AC = 6, BC = 5, de = 5.5, find the length of de. & nbsp; & nbsp; [please solve this problem from the Perspective of similar triangles,]
- 19. AB = AC = ad, ∠ DAC = 3 ∠ cab Angle BDC = 1 / 2 angle cab, angle DBC = 1 / 2 angle DAC How did you get this step?
- 20. Isosceles trapezoid ABCD, ab = CD = 5, ad = 4, BC = 10, e, f on AB, BC, EF bisects the circumference of trapezoid, BF = x, and uses X to express the area of △ bef AB DC is waist