The first volume of the eighth grade mathematics monthly exam 1. Fill in the blank: (3× 10) 1. As shown in the figure, if the straight lines a‖b, ∠ 1 = 130, then ∠2= degrees. 2. In the isosceles triangle. 3. An equilateral triangle has an axis of symmetry. 4. If the hypotenuse of RT ⊿ ABC is 6cm long, then the median line on the hypotenuse is cm.5 Given that the lengths of two line segments are 5 cm and 12 cm respectively, when the length of the third line segment is cm, these three line segments can form a right triangle. 6. If the length of one side and one hypotenuse of a right triangle are 8 cm and 10 cm respectively, then the height on the hypotenuse is greater than cm. 7. As shown in the figure, if AD‖BC, AB‖DC and ∠ A = 63, ∠C=. 8. As shown in the figure, AB‖CD, straight line EF intersects AB and CD at points E and F respectively, and bisector of ∠BEF intersects bisector of ∠DEF at point P ∠ P = .9. If the sides of an isosceles triangle are 7 cm and 4 cm respectively, then its circumference is _ _ _ _ _. Second, multiple-choice questions: (3× 10) 1 1. If ∠ α and ∠βare isomorphic angles, and ∠α = 55, ∠βis equal to () A.55 B. 125 C .55 or 125m. It is impossible to determine12. In the figure below, what is not necessarily an axisymmetric figure is () A. Line segment B. Angle C. Right triangle D. Isosceles triangle 13. According to the following conditions, it cannot be judged that two right-angled triangles are congruent () A. Two right-angled sides are equal. The acute angle is equal to the hypotenuse. The two acute angles are equal. As shown in the figure, △ AB=AC, and the points above AC are DE⊥AC and EF⊥BC. If ∠BDE= 140, ∠ DEF = () (a) 55 (b) 60 (c) 65 (d). 、∠B=60？ (B)∠A=50？ 、∠B=80？ (C)AB=AC=2, BC=4 (D)AB=3, BC=7, and the circumference is 13 16. If the top angle of an isosceles triangle is equal to 70o, then its bottom angle is () a, 70o B, 55o C, 60o D, 70o or 55o. It is correct that () ① An isosceles triangle with an angle of 60 is an equilateral triangle; (2) a triangle with three sides of 1, and 3 is a right triangle; (3) A triangle whose median line is equal to half of this side is a right triangle; ④ A triangle with the ratio of three angles of 3: 4: 5 is a right triangle; ⑤ A point with equal distance on both sides of an angle, on the bisector of this angle, A. 1 B.2 C.3 D.4 18. The following statements are correct: () A. Isomorphism angle is equal to B. Internal dislocation angle is equal to C. Opposite vertex angle is equal to D. The internal angle on the same side is complementary to 19. It is known that the base BC of isosceles △ABC is 8 cm. Then the length of waist AC is () A. 10cm or 6cm B, 10cm C, 6cm D, 8cm or 6 cm 20. There is a small P on the plane of the regular triangle ABC, which makes ⊿PAB, ⊿PBC and ⊿PCA all isosceles triangles. Then () (A) 1 point (B)4 points (C)7 points (D) 10 points. 3. Solve the problem (60 points) 2 1. (6 points) As shown in the figure, AD ‖ BC and ∠ 654438 are known. And fill in the corresponding bases in the brackets: ∫ ad ∫ BC (known), ∴1= ∠ 3 (), ∫ 1 =∠2 (known), ∴. 23.(6 points) As shown in the figure, it is known that in the middle,,, BD is the bisector of the angle, and the degree is .24. (8 points) As shown in the figure, it is known that ∠EAC is the external angle of △AD‖BC, ∠ 1 =∞. 25.(8 points) As shown in the figure, where AB=AC, two angular bisectors BD and CE intersect at point O, is (1)OB equal to OC? Please explain your reasons; (2) If AO is connected and the BC side of AO extends to point F .. What do you find? Please write two reasonable findings and write a reasoning process about one of them to confirm your findings. 26.(8 points) As shown in the figure, in △ABC and △ABD, AC⊥BC, AD⊥BD and E are the center lines on the side of AB. Try to judge whether DE and CE are equal, and explain the reasons. 27.(8 points) The Regulations of the People's Republic of China on Road Traffic Management stipulates that the speed of a car on a city street shall not exceed km/h, as shown in the figure, a car is driving on a straight road on a city street, and at a certain moment, it just drives to a place a few meters in front of the speedometer. One second later, the distance between the car and the speed detector was measured as 100 meter. Was the car speeding? 28.(8 points) At Rt⊿ABC, ∠c = 90, ∠A, ∠B and ∠ C, the lengths of the opposite sides are A, B and C respectively. Let ⊿ABC have an area of S and a perimeter of L, (1 (3) state the reason for the conclusion in (2).