In the isosceles trapezoid ABCD, the extension lines of AD / / BC, de / / AC and BC intersect at the point E, CA bisects ∠ BCD, and proves ∠ B = 2 ∠ E

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• 1. As shown in the figure, if the quadrilateral ABCD is trapezoid, ad ‖ BC, CA is bisector of ∠ BCD, and ab ⊥ AC, ab = 4, ad = 6, then tanb = () A. 23B. 22C. 114D. 554
• 2. As shown in the figure, in the right angle trapezoid ABCD, ad ‖ BC, ab ⊥ BC, ∠ DCB = 75 °, the other vertex e of equilateral △ DCE with CD as one side is on the waist ab. (1) calculate the degree of ∠ AED; (2) prove: ab = BC
• 3. As shown in Figure 1, in the rectangular trapezoid ABCD, ad ‖ BC, ab ⊥ BC, ∠ DCB = 75 ° and the other vertex e of equilateral △ DCE with CD as one side is on the waist ab (1) (2) AB = BC; (3) as shown in Figure 2, if f is a point on the line CD, ∠ FBC = 30 °, the value of dffc can be obtained
• 4. As shown in the figure, in the right angle trapezoid ABCD, ad ‖ BC, ab ⊥ BC, ∠ DCB = 75 °, the other vertex e of equilateral △ DCE with CD as one side is on the waist ab. (1) calculate the degree of ∠ AED; (2) prove: ab = BC
• 5. In trapezoidal ABCD, AD / / BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB 1) Find out all the similar triangles in the graph and prove them; 2) Let BD = x, be = y, find the analytic expression of Y with respect to x, and write out its domain of definition; 3) When ad = 4, find the length of be
• 6. As shown in the figure: in ladder ABCD, ad is parallel to BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB (1) Find out all the similar triangles in the graph and prove them (2) Let BD = x, be = y, find out the function analytic expression of Y and X (3) When ad = 4, find the length of be
• 7. As shown in the figure, in ladder ABCD, AD / / BC, point E is on diagonal BC, and angle DCE = angle ADB, if 1. In the trapezoid ABCD, AD / / BC, point E is on the diagonal BC, and angle DCE = angle ADB. If BC = 9, CD: BD = 2:3, find the length of CE. 2. In the triangle ABC, ah is perpendicular to BC, h, CF is perpendicular to AB, f, D is a point on AB, ad = ah, de / / BC, prove: de = CF 3. After cutting a square from a rectangle, the remaining rectangle is similar to the original rectangle, and find the ratio of the short side to the long side of the original rectangle
• 8. As shown in the figure, in the quadrilateral ABCD, ab = ad, AC bisects ∠ BCD, AE ⊥ BC, AF ⊥ CD. If there are triangles congruent with △ Abe in the figure, please explain the reason
• 9. In the quadrilateral ABCD, ∠ ADB = ∠ ABC = 105 ° and ∠ DAB = ∠ DCB = 45 ° prove: CD = ab
• 10. In quadrilateral ABCD, connect AC and BD, angle DAB = angle DCB = 45 °. BD vertical CD. Triangle ABC area 4.5, calculate ab
• 11. In trapezoidal ABCD, ad ‖ BC, ab = AC, if ∠ d = 110 °, ACD = 30 °, then ∠ BAC is equal to () A. 80°B. 90°C. 100°D. 110°
• 12. It is known that in the quadrilateral ABCD, AD / / BC, angle BAC = angle D, and point E.F BC.CD And QE AEF = angle ACD
• 13. As shown in the figure, in the quadrilateral ABCD, it is known that ∠ a = ∠ B = 90 ° e picks up the midpoint of AB, ∠ EDC = ∠ ECD, and proves that the quadrilateral ABCD is a rectangle. As shown in the figure (the figure can't be uploaded, but it is roughly a quadrilateral that looks like a rectangle, and the midpoint e connects the fixed points D and C to form a triangle)
• 14. In the quadrilateral ABCD, BD is perpendicular to ad, AC is perpendicular to BC, e is the key point of AB, and the verification angle EDC = angle ECD Wait online. It's urgent
• 15. Known: as shown in the figure, in trapezoidal ABCD, AB is parallel to CD, AC is vertical to BC, ad is vertical to BD, e is the midpoint of AB, prove: angle ECD is equal to angle EDC
• 16. In rectangular ABCD, ab = 4, ad = 2, point m is the midpoint of AD. point E is a moving point on edge ab. connect EM and extend the intersection line CD at point F, cross m to make the vertical line of EF, the extension line of BC at point G, connect eg, and the intersection side DC at point Q. let the length of AE be x and the area of triangle EMG be y (1) Find the tangent value of ∠ MEG; (2) Find the analytic expression of Y with respect to x, and write out the value range of X; (3) The midpoint of Mg is denoted as point P and connected with CP. if {PGC} efq, find the value of Y
• 17. As shown in the figure, in rectangle ABCD, ab = 3, BC = 4, e is the moving point on edge ad, f is a point on ray BC, EF = BF and intersecting ray DC at point G, let AE = x, BF = y (1) When △ bef is an equilateral triangle, find the length of BF (2) Find the analytic expression of the function between Y and X, and write out its domain of definition (3) Fold △ Abe along the straight line be, and point a falls at a '. Try to explore whether △ a'bf can be an isosceles triangle? If so, ask for the length of AE; if not, explain the reason As long as the answer and steps of the third question
• 18. Trapezoid ABCD is right angle trapezoid, AB / / DC, ∠ DAB = 90 °, PA ⊥ plane ABCD, and PA = ad = DC = & frac12; ab = 1, M is the midpoint of Pb, find the dihedral angle formed by plane AMC and plane BMC
• 19. As shown in the figure, in the trapezoidal ABCD, AD / / BC, ∠ ABC = 60 °. ∠ DCB = 30 ° AB = 4, find BC ad
• 20. In rectangular trapezoid ABCD, ab ∥ CD, ad ⊥ DC, ab = BC, and AE ⊥ BC