First, multiple choice questions
The root of equation (x- 1) (x+2) = 0 is ().
a、x 1= 1 x2=-2 B、x 1=- 1 x2=2
c、x 1=- 1 x2=-2 D、x 1= 1 x2=2
2, the following two triangles, must be congruent is ()
A, there are two isosceles triangles b and two equilateral triangles with angles of 40 and equal waists.
C, two isosceles triangles with angles of 100 and equal bottoms.
D, two isosceles triangles with equal sides and internal angles.
3. equation x? -x+2 = 0 root is ()
A. there is only one real number root B. There are two equal real roots.
C. there are two unequal real roots. D. there is no real root
4. equation x? After the left side of +6x-5=0 is completely squared, the equation is ().
a 、( x+3)？ = 14 B 、( x-3)？ = 14
C, (x+6)? None of the above answers are correct.
5. As shown in the figure, D is on AB, E is on AC, and AB = AC, then
After adding one of the following conditions, the clause of △ Abe △ ACD cannot be determined.
This work is ()
a、AD=AE
b、AEB=∠ADC
c、BE=CD
d、BD=CE
6. As shown in the figure, in △ABC, AB=BD=AC and AD=CD, then the degree of ∠BAC is ().
a、 100 B、 108
c、 120 D、 150
7. At the party, three students, A, B and C, stood on the three vertices of a triangle. They are playing a game of grabbing stools and asking for a wooden stool among them. Whoever grabs the stool first wins. In order to make the game fair, the most suitable position of the stool should be △ABC ().
A, the intersection point of the trilateral midline B and the intersection point of the three angular bisectors
C, the intersection point d of three sides and the intersection point of the vertical lines of three sides.
8. if the quadratic equation of x is x? The two roots of +px+q=0 are x 1=3 and x2= 1 respectively, so this unary quadratic equation is ().
a、x？ +4x+3=0 B、x？ -4x+3=0
c、x？ +4x-3=0 D、x？ -4x-3=0
9. In the figure shown in the figure, all quadrangles are squares.
All triangles are right-angled triangles, the largest of which is a square.
The side length of is 7 cm, then the shadow squares a, b, c and d
The sum of the areas is ().
a、28 B、49 C、98 D、 147
10, equation 2x about x? Two of +MX- 1 = 0 are opposites, so the value of m is ().
a、0 B、2
c、 1 D 、-2
1 1, the drawing of the angle bisector is based on the drawing of two congruent triangles. As can be seen from the figure, the basis for judging the coincidence of the constructed two triangles is ().
a、HL B、ASA
c、SAS D、SSS
12, if about the quadratic equation kx? If -6x+9=0 has two unequal real roots, then the value range of k is ().
a、k< 1 B、k≠0
C, k < 1 and k≠0 D, k > 1.
Second, fill in the blanks
13, the three sides of a right triangle are 3, 4 and x, then x=
14, about the quadratic trinomial 4x of x? +mx+ 1 is completely flat, then m=
15, the lengths of two sides of the triangle are 8cm and 6cm respectively, and the length of the third side is the equation x? A real root of-12x+20 = 0, then the area of the triangle is.
16, the equation (m+1) x | m |+(m-3) x-1= 0 is a quadratic equation about x, then m=
17. If the unary quadratic equation about x has real roots, the range of values is
18, as shown in the figure, in Rt△ABC, ∠ B = 90, ∠ A = 40,
The perpendicular lines MN and AB of AC intersect at point D, then
The degree of ∠BCD is.
Map number 18
19 as shown in the figure, in equilateral △ABC, BD=CE, and AD and BE intersect at point P, then the degree of ∠APE is ().
20. As shown in the figure, in the quadrilateral ABCD, diagonal AC and BD intersect at point E. If AC bisects ∠DAB, and AB=AC, AC=AD, there are four conclusions as follows: ① AC ⊥ BD; ②BC = DE； ③∠DAB = 2∠DBC；
④△ABC is a regular triangle. Please write the serial number of the correct conclusion.
First, multiple choice questions
The title is123455678911112.
answer
Second, fill in the blanks
13、 14、 15、
16、 17、 18、
19、 20、
Third, answer questions.
2 1, (6 points) As shown in the picture, a shepherd boy is releasing his horse at A, 4 kilometers south of the river. He is located 7 kilometers north of his hut B. He wants to take his horse to the river to drink water and then go home. What is the shortest distance for him to finish this task? (Draw and calculate)
22.( 16 points) Solve the equation
①(2x- 1)？ =9 ②x(x+2)=2(x+2)
③(x+8)(x+ 1)=- 12 ④
23.(8 points) It is known that points B, F, C and E are on the same straight line, AC and DF intersect at point G, AB⊥BE, and the vertical foot is B, DE⊥BE, and E, AB = DE, BF = CE.
Verification: (1) △ ABC △ def
(2)AG=DG
24, (6 points) known equation x? One root of +kx+ =0 is–1. Find its other root and the value of k.
25.(8 points) Known: as shown in the figure, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium.
(1) verification: BF = AC
(2) Verification: BF = 2CE；;
26.(6 points) Read the following example, please refer to the solution of the example to solve the equation X? -|x- 1|- 1=0。
Example: solving equation x? -|x|-2=0
Solution: (1) When ≥0, the original equation becomes,
Solution: (Not conforming to the problem, discarded).
(2) When < 0, the original equation becomes,
Solution: (Not conforming to the problem, discarded).
The root of the original equation is
27.( 10) It is known that the bisector of 1, △ ABC and ∠ACB intersect with the angular bisector of ∠ABC at F, and the parallel lines passing through F and BC intersect at D and E respectively.
① What is the relationship between line segment DE, BD and DF? Write and prove.
(2) As shown in Figure 2, if point F is the intersection of the bisector of the outer corner of ∠ABC and the bisector of the outer corner of ∠ACB, BD = 4 and CE = 3, find DE.
(3) As shown in Figure 3, if point F is the intersection of the bisector of ∠ABC and ∠ACB, is the conclusion in (1) still valid? If yes, please give proof; If not, please find a new conclusion and give proof.
Figure 1 Figure 2 Figure 3