Fill in the blanks
1. The isosceles triangle is a _ _ _ _ _ _ symmetrical figure, and it has at least _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
2. As you can see from the rearview mirror of a car, the last five digits of a car's license plate are _ _ _ _ _ _ _ _.
3. As shown in Figure 7, BD⊥AC is in area D, CE⊥AB is in area E, and BD=CE. According to "HL" and "AAS", it can be proved that congruent triangles is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _; On this basis, it can also be proved that congruent triangles is _ _ _ _ _ _ _ _.
Figure 7
4. As shown in Figure 8, given that OP is the bisector of ∠AOB, PC⊥OA is in C, PD⊥OB is in D, PD=3cm, OC=5cm, the area of quadrangular PCOD is _ _ _ _ _ _ _ _ _.
Figure 8
5. As shown in the figure, in △ABC, AB=AC, D is the midpoint of BC, if ∠ BAC = 124, ∠ Bad = _ _ _ _ _ _ _ _ _
Figure 9
6. Fill in the missing conditions or reasons in the reasoning process to make the conclusion effective.
As shown in figure 10, in △ABC and △ADC,
∴△ABC≌△ADC(SAS)
Figure 10
7. The points with equal distances to the three sides of the triangle are the intersections of the triangle _ _ _ _ _ _ _ _.
8. As shown in the figure, DE is the middle vertical line of the side AC of Rt△ABC, ∠ C = 90, AB = 5°, BC = 3°, then the circumference of △BCE is _ _ _ _ _ _ _ _ _.
9. As shown in the figure, the line segment AB and the line segment are symmetrical about Y, the coordinate is a (3 3,2), and it is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
10. As shown in the figure, L is the symmetry axis of quadrilateral ABCD. If AD//BC, we can draw the following conclusions: ① AB//CD; ②AB = BC； ③ab⊥bc； ④ ao = co. The correct conclusion is _ _ _ _ _ _ (fill in the serial number of the conclusion you think is correct).
Second, multiple choice questions
1 1. The national flags of some countries are designed as axisymmetric figures. In the national flag of Shikoku in figure 1, do you think the axisymmetric figure is ()?
Figure 1
A.4b 3c 2d 1
12. As shown in Figure 2, P is a point on the bisector of ∠BAC, PM⊥AB is at M, and PN⊥AC is at N, so the following conclusion is correct ().
Figure 2
①PM=PN ②
③ The areas of △ APM and △APN are equal; ④ ∠ Pan+∠ APM = 90。
A. 1 B. 2 C. 3 D.4
13. In △ ABC and △, ①AB=, ②, ③, ④∠A=, ⑤, ⑤∠C =∞, then the following condition that △ ABC △ cannot be proved is ().
A.①②③ B. ①②⑤ C. ①②④ D. ②⑤⑥
14. If two points are symmetrical about x axis, the value of is ().
A. 16 B. 4 C. D
15. The following statement is true ()
① The bisectors of the height, midline and angle of an isosceles triangle coincide.
② The length of the midline of the isosceles triangle is equal.
③ The waist of an isosceles triangle must be higher than its waist.
④ If one side of an isosceles triangle is 8 and the other side is 16, then its circumference is 32 or 40.
A. 1 B. 2 C. 3 D.4
16. In △a, B and C, the lengths of the three sides are A, B and C respectively. If so, the triangle must be ().
A. isosceles triangle
C. isosceles right triangle D. None of the above answers are correct
17. as shown in figure 3, a is on DE, f is on AB, AC=CE, ∠ 1=∠2=∠3, then the length of DE is equal to ().
Figure 3
A.b . b . c . AB d . a b+ AC
18. As shown in Figure 4, the three bisectors of equilateral triangle ABC intersect at point O, OD//AB intersect at point D BC, and OE//AC intersect at point E BC, then the isosceles triangle * * in this figure has ().
Figure 4
A.4 B. 5 C. 6 D.7
19. As shown in Figure 5, AB and DC intersect at point E, EA=EC, DE=BE. To make △ AED△ CEB, then ().
Figure 5
A. the condition of ∠A=∠C should be added. B. the condition of ∠B=∠D should be added.
C. No supplementary conditions are needed. D. None of the above statements are correct.
20. As shown in Figure 6, △DAC and △EBC are equilateral triangles, and AE and BD intersect with CD and CE at points M and N respectively. Draw the following conclusions:
①△ACE?△DCB； ②CM = CN； ③AC=DN .
Among them, the number of correct conclusions is ()
Figure 6
A.3 B. 2 C. 1 D.0。
Third, answer questions.
2 1. As shown in figure 1 1, it is known that ∠ ACB = ∠ ADB = 90, BC=BD, and e is any point on AB. Proof: CE=DE.
Figure 1 1
22. as shown in fig. 12, in △ABC, AB=AC, ∠ BAC = 50, point p is within △ABC, ∠ 1=∠2, and find the degree of ∠BPC.
Figure 12
23. As shown in figure 13, please take two of the following four conditions as known conditions and the third as the conclusion to derive a correct proposition. (Write only one situation)
Figure 13
①AE=AD ②AB=AC ③OB=OC ④∠B=∠C
Reference answer
1. axis, 1, countless 2s. BA629 3。 △ European Central Bank, △DBC, △ EOB △ Doc.
4. 15cm2 5。 62 6.∠ DCA = ∠ BCA 7。 Vertical parallel lines
8.8 9.(-3,2),( 1,-4) 10.①②④
1 1.C 12。 D 13。 C 14。 C 15。 B 16。 B 17。 B 18。 D 19。 C 20。 C
2 1.∠∠ACB =∠ADB = 90, in Rt△ACB and Rt△ADB, BC=BD, AB=AD. ∴△ACB≌△ADB(HL)∴CE=DE (the corresponding sides of congruent triangles are equal)
22.∵AB=AC, ∴△ABC is congruent triangles, ∴∠ B = ∠ C.
∠∠BAC = 50，∠B=∠C
∴∠B=∠C=( 180 -50 )÷2=65
∵∠ 1=∠2. So ∠ 1+∠ BCP = 65.
∴∠bpc= 180-65 = 1 15
23.∫In△ACD and △ABE, AB=AC (known), ∠A=∠A (male * * * angle), AE=AD. ∴△ACD≌△ABE(SAS)。 ∴∠B=∠C (the corresponding angles of congruent triangles are equal).
grade
Grade?Eight
subject
mathematics
version
periodicity
Content title
The ninth middle school of Mudanjiang City, Heilongjiang Province, 2008-2009 school year, the first monthly examination paper of mathematics in the eighth grade last semester (universal version)
Classification index number
G.624.6
Classification index description
Test questions and solutions
key word
The ninth middle school of Mudanjiang City, Heilongjiang Province, 2008-2009 school year, the first monthly examination paper of mathematics in the eighth grade last semester (universal version)
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