As shown in the figure, ab = AE, BC = ed, ∠ B = ∠ e, AF ⊥ CD, foot drop is f, which means that AF bisects CD
Make auxiliary line AC, ad
Because AB = AE, BC = ed, ∠ B = e (edge)
So triangle ABC = triangle AED (congruent)
So AC = ad
So triangle ACD is isosceles triangle
Therefore, ACF = ADF
Because AF ⊥ CD
Therefore, AFC = AFD = 90 degree
Because AC = ad, ACF = ADF, AFC = AFD (corner side)
So triangle AFC = triangle AFD (congruent)
So CF = DF
RELATED INFORMATIONS
- 1. In the Pentagon ABCDE, if angle a = angle c = 90 degrees, ab = BC = de = AE + CD = 3, what is the area of the Pentagon?
- 2. As shown in the figure, in the Pentagon ABCDE, BC = 4, CD = 4-ab, AE = de = 6, AE ⊥ AB, de ⊥ CD______ .
- 3. As shown in the figure: ab = AE, BC = ed ∠ B = ∠ E. verify that ∠ C = ∠ D is a Pentagon, and the counter clockwise letter is ABCDE
- 4. In the pentagonal ABCDE, ∠ A is 135 ° AE ⊥ ed, ab ∥ CD, ∠ B = ∠ D, try to find the degree of ∠ C
- 5. AB = AE, BC = ed in Pentagon ABCDE Angle BCD = BAE = EDC = 120, is AC equal to ad AB = root 3 BC = 1
- 6. Known: as shown in the figure, in the Pentagon ABCDE, angle B = angle e = 90, ab = CD = AE = BC + de = 4 Finding the area of Pentagon
- 7. As shown in the figure, in the Pentagon ABCD, ab = CD = de = BC + AE = 2, angle B = angle e = 90 degrees, find the area of the Pentagon ABCD De Level is not enough, no picture
- 8. It is known that: as shown in the figure, in △ ABC, ∠ C = 90 °, cm ⊥ AB in M, at bisection ∠ BAC intersects cm in D, intersects BC in T, de ∥ AB through D intersects BC in E, verification: CT = be
- 9. It is known that: as shown in the figure, in △ ABC, ∠ C = 90 °, cm ⊥ AB in M, at bisection ∠ BAC intersects cm in D, intersects BC in T, de ∥ AB through D intersects BC in E, verification: CT = be
- 10. It is known that in the triangle ABC, D and E are points on AB and AC respectively, and de / / BC, be and CD intersect at point O, and the extension line of Ao intersects with BC at point M=
- 11. It is known that ab = AE, BC = ed, AF is the vertical bisector of CD, as shown in the figure
- 12. As shown in the figure, in the pentagonal ABCDE, ∠ BAE = 120 °, ∠ B = ∠ e = 90 °, ab = BC, AE = De, find a point m and N on BC and de respectively to minimize the perimeter of △ amn, then what is the degree of ∠ amn + ∠ anm
- 13. As shown in the figure, in the pentagonal ABCDE, ∠ BAE = 120 °, ∠ B = ∠ e = 90 °. AB = BC, AE = De, find a point m, N on BC, de respectively, so that the perimeter of △ amn is the smallest, then the degree of ∠ amn + ∠ anm is () why extend AB to a 'to make Ba' = AB, extend AE to a 'to make AE = EA' ', connect a'm, a'n, then the perimeter of △ amn is the smallest?
- 14. As shown in the figure, in the Pentagon ABCDE, BC = De, AE = DC, angle c = angle e, DM is perpendicular to AB and M is the midpoint of ab
- 15. As shown in the figure, in the regular pentagon ABCDE, ab = AE, BC = ed, angle B = angle e, and point F is the midpoint of CD
- 16. As shown in the figure, ab = AE, angle B = angle e, BC = ed, f is the midpoint of CD, and verify that AF is vertical to CD
- 17. As shown in the figure, ab = AE, BC = ed. ∠ B = ∠ E. f is the midpoint of CD. Explain the reason why AF ⊥ CD .A one 1 1 1 1 1 1 1 1 1 1 1 1 B 1 1 1 E 1 1 1 1 1 1 one hundred and eleven million one hundred and eleven thousand one hundred and eleven C F D
- 18. As shown in the figure, the angle B = ∠ C = 90 °, M is a point on BC, and DM bisects ∠ ADC, am bisects ∠ DAB, proving: ad = CD + ab
- 19. In trapezoidal ABCD, ad is parallel to BC, triangle ADC is 2:3 than triangle ABC, and the connecting line of diagonal midpoint m and N is 10 cm Finish it today as soon as possible
- 20. In trapezoid ABCD, ab ‖ CD, ∠ ABC = 90 °, ab = 5, BC = 10, Tan ∠ ADC = 2. (1) find the length of DC; (2) e is a point inside the trapezoid, f is a point outside the trapezoid, if BF = De, ∠ FBC = ∠ CDE, try to judge the shape of △ ECF, and explain the reason. (3) under the condition of (2), if be ⊥ EC, be: EC = 4:3, find the length of de