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
∵∠ hem = ∠ AEH, ∵ bef = ∠ FEM, ∵ HEF = ∠ hem + ∠ FEM = 12 × 180 ° = 90 °, ∵ HF = Eh2 + ef2 = 32 + 42 = 5, ∵ EM = 3 × 4 △ 5 = 2.4, ∵ AB = AE + be = EM + Em = 4.8cm
RELATED INFORMATIONS
- 1. 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
- 2. If eh = 3, EF = 4, what is the length of edge ad
- 3. 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)
- 4. In cuboid, abcd-efgh, ab = 9cm, BC = 5cm, BF = 5cm BF = 4cm / find the total length of the edge perpendicular to the plane dcgh
- 5. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ .
- 6. 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
- 7. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ .
- 8. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ .
- 9. As shown in the figure, in ladder ABCD, ad ‖ BC and EF are the midpoint of AB and AC respectively. Connect EF and intersect AB and CD with G and h to verify: (1) eh = GF; (2) Hg = 1 / 2 (BC-AD)
- 10. Given that the space quadrilateral ABCD E F G is the midpoint of AB BC CD ad respectively, we prove the efgh parallelogram
- 11. 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
- 12. 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?
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. 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?
- 18. 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
- 19. 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
- 20. In the isosceles trapezoid ABCD, AD / / BC, assuming BC = 4, ad = 8, angle a = 45 degrees, the area of the trapezoid is calculated