A multiple-choice question (3 points × 10 = 30 points)
1. The result of calculation is ()
A.4 B. 2 C. D
2. If known, the median term in the ratio of A and B is ()
A. 5th century BC
3. If two of the equations hold, then ()
A. 2 BC to 3 BC.
4. if c is the golden section of line segment AB, AC > BC, if ab = 1, AC = ().
A.0.6 18 BC
5. The root of the equation is ()
A.B.
C.D.
6. The following proposition is true ()
A quadrilateral with equal diagonal lines is a parallelogram.
A quadrilateral with diagonal lines perpendicular to each other and divided into two is a diamond.
A quadrilateral with four equal sides is a square.
A quadrilateral with right angles is a rectangle.
7. Every outer angle of a polygon is 30, so the number of sides of the polygon is ().
A.b . 18 c . 10d . 12
8. The price of a commodity after two consecutive price reductions 10% is one yuan, and the original price of the commodity is ().
A.B.
C.D.
9. In △ABC, d is a point on the side of AC, ∠ DBC = ∠ A, and the length of CD is ().
A. 65438 BC+2 BC.
10. As shown in the figure, in trapezoidal ABCD, e and f are the midpoint of AB and CD respectively, and AD and BC are the two roots of the equation, then EF is ().
A. 1 B. 3 C. 2 D. 4
Two. Fill in the blanks (2 points × 9 = 18 points)
1. If it is a quadratic radical, the range of x is _ _ _ _ _ _ _ _.
2. The diagonal of a square has a diamond shape, but the diagonal does not have the property of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
3. Please write a figure _ _ _ _ _ _ which is both central and axial symmetry.
4. Write a similar quadratic radical _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
5. If the equation has two equal real roots, the value of k is _ _ _ _ _ _ _ _.
6. Factorize the factors in the real number range: _ _ _ _ _ _ _ _
7. As shown in the figure, if ∠ Abd = ∠ C, write a similar triangle _ _ _ _ _ _ _ _ _ _ _.
8. If yes, then _ _ _ _ _ _ _
9. As shown in the figure, AB=CD, AD‖BC, AC⊥BD, AO = 1, CO = 2, then the height of trapezoidal AB = CD is _ _ _ _ _ _ _ _.
Three. Calculation (5 points +7 points = 12 points)
1.(5 points)
2.(7 points)
Know the value of.
4. Solve the equation (5 points +7 points = 12 points)
1.(5 points)
2.(7 points)
solve
5. Solving problems (6 points +7 points +7 points +8 points = 28 points)
1.(6 points) As shown in the figure, in right-angle ABCD, e is a point above BC, and DF⊥AE is in F, if AE = BC.
Verification: ce = Fe
2.(7 points) If the sum of the two roots of the equation about X is equal to the product of the two roots, solve the equation and find the value of m.
3.(7 points) Known: As shown in the figure, in trapezoidal ABCD, AD‖BC, E is the midpoint of AB, and CD = AD+BC.
Verification: DE⊥EC
4.(8 points) It is known that the quadrilateral ABCD is a right-angled trapezoid, AD‖BC, ∠ A = 90, point E is on AB, and ED⊥CD is on D. If, find the length of BC.
Test answer
1. Multiple choice questions.
1.B 2。 A 3。 C 4 explosive D 5。 A
6.B 7。 D 8。 D 9。 C 10。 C
2. Fill in the blanks.
1.2. The diagonals of the squares are equal.
3. rectangle 4. and
5.0 or 6.
7.△ Abd ∽△ACB
8.9.
Three. Calculate.
1. solution: original recipe
2. Solution:
4. Solve the equation.
1. solution:
2. Solution: Suppose, then the original equation is defined as
Finishing:
When was that
There is no solution to this equation.
When was that
Test: put each one in, and none of them is 0.
Is the solution of the original equation.
5. Answer the questions.
1.
Prove: ∵ quadrilateral ABCD is a rectangle.
∴BC=AD
Ae = BC, ∴ AE = AD
∴∠ 1=∠ADE
And ∠ ade+∠ 2 = 90, ∠ 1+∠ 3 = 90.
∴∠2=∠3
In Rt△DFE and Rt△DCE
∴Rt△DFE≌Rt△DCE
∴CE=FE
2. Solution: The equation can be simplified as follows
Let its two roots separate, and then
and
, namely
∴
3. proof: find the midpoint f of CD, followed by EF.
rule
and
and
4. solution: if d is DF⊥BC in f, then DF‖AB.
∴∠ 1=∠3
∠ 3 +∠ 2 = 90.
∴∠ 1+∠2=90
∠∠2+∠c = 90。
∴∠ 1=∠C
∴Rt△AED∽Rt△FCD
That is all right
and
In Rt△DFC,
that is