Known: as shown in the figure, in the isosceles trapezoid ABCD, ab = CD, ad ‖ BC, e is a point outside the trapezoid, and EA = ed, prove: EB = EC

It is proved that in the isosceles trapezoid ABCD, ab = CD, ∠ bad = ∠ CDA. ∵ EA = ed,  ead = ∠ EDA. ≌ EAB = ∠ EDC. (2 points) in △ Abe and △ DCE, ≌ AB = DC ≌ EAB = edcea = ed, ≌ Abe ≌ DCE. (5 points) ≌ EB = EC. (6 points)

RELATED INFORMATIONS

1. 1. Given that e is the midpoint of the edge BC of the parallelogram ABCD and EA = ed, it is proved that the four deformed ABCD is a rectangle 2. The bisector of an inner corner of a rectangle divides an edge of the rectangle into 6cm. What is the length of the bisector of the inner corner of the rectangle when it is 8cm? 3. In rectangular ABCD, ab = 2BC, e is a point on CD, and AE = AB, what is the degree of ∠ EBC? 4. AC is the diagonal of square ABCD, AE bisects ∠ BAC, proving: ab + be + AC 5. In rectangular ABCD, M is the midpoint of AD, CE ⊥ BM, the perpendicular foot is e, ab = 4cm, BC = 4 レ 2cm, find the length of Ce (Note: 4 レ 2 →→→ 4 times root 2) Wealth, No picture. Thank you
2. As shown in the figure, in the parallelogram ABCD, AC and BD intersect at point O, e is the outer point of the parallelogram ABCD, EA ⊥ EC, ed ⊥ be
3. As shown in the right figure, in the trapezoidal ABCD, AD / / BC, the area of triangle Abe is 30 square centimeters, EC = 2ae, calculate the area of trapezoidal ABCD The figure is trapezoid with two diagonals The order is (from left to right) ADB The focus is e
4. As shown in the figure, in the right angle trapezoid ABCD, ∠ C = 90 °, ad ‖ BC, AD + BC = AB, e is the midpoint of CD. If ad = 2, BC = 8, calculate the area of △ Abe
5. As shown in the figure, in the trapezoidal ABCD, ab ‖ CD is known, and point E is the midpoint of BC. If the area of △ DEA is S1 and the area of trapezoidal ABCD is S2, then the quantitative relationship between S1 and S2 is______ ．
6. As shown in the figure, in the trapezoidal ABCD, AD / / BC, ab = CD, e is the midpoint of BC It's in the mathematics evaluation manual of the ninth grade volume I of Jiangsu Education Press.
7. As shown in the figure, the quadrilateral ABCD is a parallelogram, and the points E and F are the points on the sides of AD and BC respectively, and AE = cf. the following are proved: (1) the △ Abe ≌ △ CDF; (2) the quadrilateral BEDF is a parallelogram
8. If the quadrilateral ABCD is a parallelogram, e and F are the points on the extension line of AC and Ca respectively, and CF = AE, what is the relationship between BF and de? Please explain the reason (2) As shown in Figure 14, in trapezoidal ABCD, ab ‖ CD, AC and BD intersect at point O. if OA = ob, try to judge the shape of trapezoidal ABCD and explain the reason
9. What is the ratio of s △ AED to s ladder ABCD if ab ‖ DC and point e are the midpoint of waist BC in ladder ABCD
10. As shown in the figure, in ladder ABCD, ab ‖ DC, ab ⊥ BC, e are the midpoint of AD, AB + BC + CD = 6, be = 5, then the area of ladder ABCD is equal to () A. 13B. 8C. 132D. 4
11. Known: as shown in the figure, in rectangular ABCD, the diagonal intersects at point O, ∠ AOB = 60 °, AE bisects ∠ bad, AE intersects BC at E. calculate the degree of ∠ BOE
12. Known: as shown in the figure, in rectangular ABCD, the diagonal intersects at point O, ∠ AOB = 60 °, AE bisects ∠ bad, AE intersects BC at E. calculate the degree of ∠ BOE
13. As shown in the figure, in the rectangle ABCD, the diagonal AC and BD intersect at the point O. is there a circle so that all four points of ABCD are on the circle? If there is one Please point out the center and radius of this circle. If it doesn't exist, explain why
14. As shown in the figure, if the diagonals of rectangle ABCD intersect at point O, AE bisector angle bad intersects BC at e, and angle CAE = 15 degrees, then the angle BOE=
15. As shown in the figure, in rectangular ABCD, AC and BD intersect at point O, AE bisects ∠ bad, BC intersects at E. if ∠ EAO = 15 °, then the degree of ∠ BOE is______ Degree
16. In rectangle ABCD, AC BD intersects with 0 AE bisector angle bad if ∠ EAO equals 15 degrees and BOE equals 15 degrees=
17. As shown in the figure, in rectangular ABCD, AC and BD intersect at point O, AE bisects ∠ bad, BC intersects at E. if ∠ EAO = 15 °, then the degree of ∠ BOE is______ Degree
18. In rectangular ABCD, diagonal lines AC and BD intersect at point O, AE bisects ∠ bad, AE intersects BC at point E. if ∠ CAE = 15 °, what is the degree of ∠ BOE?
19. In rectangular ABCD, AC and BD intersect at point O, AE bisects the angle bad, and if the angle EAO = 15 °, calculate the degree of the angle BOE I can't give you a picture
20. As shown in the figure: given rectangular ABCD, AC and BD intersect at O, AE ‖ BD, de ‖ AC. verification: OE ⊥ ad