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
(1) In ∵ equilateral △ DCE, ∵ CDE = 60 ° and ∵ ade = 45 °. ∵ ab ⊥ BC, ad ∥ BC, ∵ DAB = 90 ° and ∵ AED = 45 ° (2) ∵ right angle △ AED,
RELATED INFORMATIONS
- 1. The following polynomials can be decomposed by complete square A.x²+1 B.x²+2x-1 C.x²+x+1 D.x²+4x+4 What is the factorization of the following polynomials in Liangshan in 2012 A.x²+y² B.-x²-y² C.-x²+2xy-y² D.x²-xy+y²
- 2. A polynomial Plus + x2y-3xy2 gives the third power of x-3x2y. This polynomial is
- 3. If the solution set of inequality MX2 + MX-1 > 0 about X is an empty set, the value range of real number m is obtained
- 4. Given the set a = {a, a + D, a + 2D}, B = {a, AQ, AQ & sup2;}, (a is a known constant), if a = B, find the value of D, Q
- 5. We know that set a = {x 3} and set B = {x 4x + M
- 6. Given the set a = {x | - 5 ≤ x ≤ 3}, B = {y | = a-2x-x & sup2;}, where a ∈ R, if a is contained in B, find the range value of real number a RT
- 7. If the distance from the center O to the chord AB is a, then the diameter of O is a
- 8. A chord is divided into two parts: 1:4. Find the degree of the circumference angle of the chord
- 9. If a chord of a circle is known to divide the circle into two parts of 1:3, then the degree of the angle of the circle to which the chord is directed is______ .
- 10. Why are the same chords complementary to each other? How to prove the complementarity or equality of the circle angles of the same chord?
- 11. In the trapezoidal ABCD, AD / / BC, e is the midpoint of waist AB, de ⊥ CE
- 12. If point P is a point in the cube abcd-a'b'c'd 'with edge length 1 and AP = 3 / 4AB + 1 / 2ad + 2 / 3AA', then the distance from point P to edge length AB is_________
- 13. In the parallelogram ABCD, point m is the midpoint of AB, point n is on BD and BN = 1 / 3bd. It is proved that m, N and C are collinear 0 Use vectors if you can
- 14. In the parallelogram ABCD, a (1,1) AB vector (6,0) m is the midpoint of line AB, and the intersection of line cm and BD is p I know that the trajectory of P is a circle, but I don't know how to prove it
- 15. As shown in the figure, in the square ABCD with side length of 5 + 2, draw a sector with a as the center, draw a circle with o as the center, m, N, K as the tangent points, take the sector as the side of the cone, and take the circle O as the bottom of the cone to form a cone, and calculate the total area and volume of the cone
- 16. As shown in the figure, in the pyramid p-abcd with rectangular bottom, PA ⊥ plane ABCD, PA = ad, e is the midpoint of PD (1) verification: Pb ∥ plane AEC; (2) verification: plane PDC ⊥ plane AEC
- 17. In the cube ABCD -- a'b'c'd ', O is the center of the square ABCD on the bottom, and M is the midpoint of the line a'b Verification: plane a'bd ⊥ plane a'acc ' emergency
- 18. As shown in the figure, the area of square ABCD is 16, △ Abe is an equilateral triangle, point E is in square ABCD, and there is a point P on diagonal BD, so that the sum of PC + PE is minimum, then the minimum value is () A. 4B. 23C. 26D. 2
- 19. As shown in the figure, in the cuboid abcd-a1b1c1d1, ab = ad = 1, Aa1 = 2, and point P is the midpoint of dd1. Prove: (1) straight line BD1 ‖ plane PAC; (2) plane bdd1 ⊥ plane PAC; (3) straight line PB1 ⊥ plane PAC
- 20. As shown in the figure, in the cube abcd-a1b1c1d1, the tangent of the dihedral angle b-a1c1-b1 is___ .