4. As shown in the figure, △ABC and △ A ′ B ′ C ′ are symmetrical about a straight line, then the degree of ∠B is (★) A.30o? B.50o？ C.90o D. 100o？
5. If the real number satisfies y=, then the value is (★) a.0b. 1? C.2？ d-26。 What is the point where the three vertices of a triangle are equidistant (★)? A. What is the intersection of three bisectors? B. what is the intersection point of the midline of the three sides? C. what is the intersection point of the straight line where the height of three planes lies? D. Intersection of Trilateral perpendicular bisector 7. As shown in the figure, it is known that ∠ 1=∠2, AC=AD, and the following conditions are added: ① AB = AE; ②BC = ED； ③∠C =∠D； ④ ∠ B = ∠ E. Among them, the condition for enabling △ ABC △ AED is (★) A. 1 B.2? C. 3 D. 4 8。 Make a square with the unit long line segment of the number axis as the edge, take the origin of the number axis as the rotation center, and rotate the diagonal line passing through the origin clockwise, so that the other end point of the diagonal line falls at point A of the positive semi-axis of the number axis, then the number represented by point A is (★)? 1.4 cm.
9. As shown in the figure, point A and point B are symmetrical about X, and the coordinate of point A is (4,4), then the coordinate of point B is (★) A. (4,4)? B.(4，-2)？ C. (-2，4)d .(4，2) 10。 The volume of a cube is 99. It is estimated that its side length is between (★) A.2 and 3? B.3 to 4? Between c.4 and 5? Between d.5 and 6.
2. Fill in patiently (3 points for each question, * * 18 points, and write the result directly) 1 1. The result of calculating ~-+2 is. 12. If 25x2=36, then x =；; If so, then y =? . 13. If point P is symmetrical about X axis (3,–4), then the coordinate of point P is symmetrical about Y axis. 14. As shown in the figure, please add a condition:, so (only one can be added). 15. If the outer angles of an isosceles triangle are equal, then the top angles of the triangle are also equal. Then cut one of them into four smaller regular triangles in the same way, and so on. The result is as follows: the tangent number is 1 2 3 4 … n The number of regular triangles is 471kloc-0/3 … an.
Then an =? (represented by an algebraic expression containing n). 3. Calculation problems (be careful in calculation and be good at thinking! There are three small questions in this big question, ***24 points) 17. (8 points) Calculation? 18.(8 points) As shown in the figure, simplify the real number and its position on the number axis.
19.(8 points) As shown in the figure, ABC and BD are divided into equal parts ∠ABC, ∠ A = 120, ∠ C = 60, AB=CD=4cm, and the perimeter of the quadrilateral ABCD is found.
4. Answer questions (this big question has three small questions, with ***26 points) 20. (8 points) In order to build flower beds in the rectangular open space for greening in residential areas, the required design patterns are composed of isosceles triangles and squares (unlimited in number), and the whole rectangular space is axisymmetric. Do you have a good design? Please draw your design in the rectangle as shown. ? 2 1.(8 points) As shown in the figure, in the plane rectangular coordinate system,? (1).(2) Make a symmetrical figure about the axis of the figure. (3) Write the coordinates of points A 1, B 1 and C 1.
22.( 10) It is known that △ABC is an equilateral triangle, and D is any point on AB, connecting BD. (1) At the lower left of BD, make an equilateral triangle BDE (draw with a ruler, keep drawing traces and don't write) (2) Connect AE, and verify: CD = AE?
5. solving problems (learning mathematics should be good at observing and thinking, and dare to explore! There are two small problems with this topic, ***22 points) 23. (10) As shown in the figure, at △ABC, AD⊥BC, point E is on the perpendicular line of AC, and BD=DE. (1) If BAE = 40, then ∞. (2) If the circumference of △ABC is 13cm and AC is 6cm, then the circumference of △ABE is _ _ _ _ _ _ cm (3) You find that the sum of line segments AB and BD is equal to the length of which line segment in the figure, which proves your conclusion.
24.( 12 minutes) Right-angled triangle () rotates counterclockwise around the right-angled vertex? (), and then folded along the opposite side, intersecting at the point, and? Intersect at point, intersect at point. (1) Proof:. (2) Find out the quantitative relationship between sum and explain it. The answers to the final review questions in the first volume of the eighth grade (1)
1. Choose one carefully (the title is *** 10, with 3 points for each question and 30 points for * * *. )
The question number 1 234556789 10 answers ABC, DC, DC, DC, DC, and DC.
2. Fill in patiently (3 points for each question, * *18 points, and write the result directly).
1 1.？ + ? 12.； -8. 13.(-3,4) 14.①BC = AD； ②∠ABC =∠DAB； ③∠C =∠D； ? ④AC = BD； ..... (add one at random) 15. 700 or 400? 16.3n+ 1
3. Calculation problems (be careful in calculation and be good at thinking! There are three small questions in this big question, ***24 points)
17.(8 points) Calculation:? = 2-4+4× = 2-4+2 = 0 18.(8 points) As shown in the figure, the position of real numbers on the number axis is simplified. =-a-b-(a-b)=-a-b-a+b =-2a 19。 (8 points) ∵ AD ∨ BC ∴ ADB = ∠ DBC? ∠ADC+∠C= 1800？ ∠ADC = 1500∠ABD =∠DBC？ ∠A= 120？ ∴∠adb=∠abd = 300∠BDC =∠ADC-∠adb=900∴ad = ab = 4cm
At Rt△BCD, ∵ DBC = 300 ∴ BC = 2cd = 8cm, ∴ AB+BC+CD+DA = 20cm.
4. Answer questions (there are three small questions in this big question, with ***26 points)
20.(8 points) (omitted) 2 1. (8 points) (1)(2 points) S△ABC = (2)(3 points) (omitted) (3 points) A 1 (1, 5.
22.( 10) (1)△BDE is what you want. (4) (2)(6) (omitted)
5. solving problems (learning mathematics should be good at observing and thinking, and dare to explore! This big problem has two small problems, ***22 points)
23. (10) (1) (2) ∠ b = _ 70 _ _, ∠ c = _ 35 _ _ (2) △ Abe circumference = _ _ 7 _ _ cm.
24.( 12)( 1)(6) (omitted) (2)(6) When appropriate, =? Proof: (omitted)