In trapezoidal ABCD, CD is equal to AB, if angle a = 45 degrees, angle B = 60 degrees, BC = 5, find the length of AD and ab

The length of ad is 4 root sign 2 and ab is 14. The solution is to extend the lines AD and BC to form a crossing point e to form a triangle, then make a vertical line from e to AB, and finally make a vertical line from C to ab. the two vertical lines in this way are parallel lines, and then be understood by Pythagorean

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1. In the trapezoid ABCD, AB is parallel to BC, the diagonal AC is perpendicular to BD, and AC is equal to 8 cm, BD is equal to 6 cm. What is the height of this trapezoid?
2. In the trapezoidal ABCD, if ad ‖ BC, diagonal AC ⊥ BD, and AC = 6cm, BD = 8cm, the length of the trapezoidal median line is equal to
3. As shown in the figure, the four corners of rectangle ABCD are folded inward to form a seamless and overlapping quadrilateral efgh. If eh = 3cm and EF = 4cm, the length of side AB is () A. 4.6cmb. 4.8cmc. 5.0cmd
4. As shown in the figure, fold the four corners of rectangle ABCD inward to form a seamless quadrilateral efgh, eh = 12cm, EF = 16cm, then the length of side ad is () A. 12 cm B. 16 cm C. 20 cm D. 28 cm
5. If eh = 3, EF = 4, what is the length of edge ad
6. As shown in the figure, in the cuboid abcd-efgh, ab = BC = CD = Da = 4cm, FB = 3cm, if ant a walks 6cm per second, ant B walks 5cm per second (2) If ant a starts from point a, moves along the edge in the plane ABCD, and then goes back to point a (not in motion), ant B starts from point F, moves down along the edge FB, and then moves along the edge in the plane ABCD to point a (not in motion), and two ants start at the same time, then where do they meet? (except point a) (there are three answers)
7. In cuboid, abcd-efgh, ab = 9cm, BC = 5cm, BF = 5cm BF = 4cm / find the total length of the edge perpendicular to the plane dcgh
8. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
9. When the quadrilateral ABCD satisfies what condition, the quadrilateral efgh is a rectangle, and EF = 2fg? And explain the reason E F G H is the midpoint of the segment AB BC CD ad respectively
10. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
11. P is any point on the side BC of the square ABCD, and PE is perpendicular to BD intersecting BDE, PF is perpendicular to AC intersecting AC, if AC = 10, EP = FP
12. In isosceles trapezoid ABCD, ad is parallel to BC, ab = CD, P is a point on BC, PE is parallel to CD, AC intersects with E, PF is parallel to AB, BD intersects with F
13. As shown in the figure, in ladder ABCD, ad ∥ BC, ∠ C = 90 ° and ab = ad. connect BD, make a vertical line of BD through point a, intersect BC at point E, and the vertical foot is h. if EC = 3cm, CD = 4cm, calculate the area of ladder ABCD
14. Let AB = a, ad = B, BC = 2B (a > b). Make de ⊥ DC, de intersect AB at point E, connect EC. (1) try to judge whether △ DCE and △ ade, △ DCE and △ BCE are similar. (2) for the above judgment, if the two triangles must be similar, please prove it. (3) if not, please point out when a and B satisfy what relationship, they can be similar?
15. As shown in the figure, in the trapezoidal ABCD, ad ‖ BC, ∠ B = 90 °, ab = 4cm, ad = 18cm, BC = 21cm, point P starts from point a, moves 2cm / s along edge ad to point D, point Q starts from point C, moves 6cm / s along edge CB to point B, P and Q start at the same time, if one point moves to the end point, the other point stops=______ Cm; 2______ Second, PQ = CD
16. As shown in the figure, in the trapezoidal ABCD, ad ‖ BC, ∠ B = 90 °, ab = 14cm, ad = 18cm, BC = 21cm, point P starts from point a, moves at 1cm / s along side ad to point D, and point Q starts from point C, moves at 9cm / s along side CB to point B. If one point moves to the end point, the other point stops. If P and Q start at the same time, can a quadrilateral PQCD become an isosceles trapezoid? If so, how many seconds? If not, please give reasons
17. In the isosceles trapezoid ABCD, AD / / BC, assuming BC = 4, ad = 8, angle a = 45 degrees, the area of the trapezoid is calculated
18. In the trapezoidal ABCD, ab = 8, ad = 5, CD = 6, BC = 15. Point E is on the bottom BC, and point F is on the waist CD. EF bisects the area and perimeter of ABCD at the same time to find the length of CE
19. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference
20. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference