If the right side of a right triangle is 1 1 and the other two sides are continuous natural numbers, then its circumference is _ _ _ _. It is known that ∠ c = 90 in Rt△ABC. (1) If a=3 and b=4, then C = _ _ _ _ _ (2) If a = 40 and b = 9, then C = _ _ _ _ _ (3) If a = 6 and c = 10, then B. Exercise 2 (Fill in the blanks) Rt△ABC, ∠ C = 90, AB = 10 is known. (1) If ∠ a = 30, BC = _ _ _ _ _, AC = _ _ _ (2) If ∠ A = 45, BC = _ _ _ _ _ _ _ _. Exercise 3 It is known that the side length of equilateral triangle ABC is 6cm. Found: (1) the length of high AD; (2) the area of △ ABC. 1. Fill in the blanks (3 points for each blank, counting 30 points) 1. In Rt△ABC, ∠ C = 90 (1) If A = 5 and B = 12, then C = _ _ _ (2) If b = 8 and c = 17, then S △ ABC = _ _. 2. If the bottom of the ladder is 9m away from the building, the height of the building reached by the ladder with the length of 15m is _ _. 3. If the ratio of three sides of a triangle is 45: 28: 53, then the triangle is _ _ _ _ (classified by angle). 4. In △ABC, if the lengths of its three sides are 9, 12 and 15 respectively, the area of a rectangle composed of two such triangles is _ _ _ _. 5. In △ABC, if AB = AC = 17cm, BC = 16cm, and AD ⊥ BC is in D, then AD = _ _ _. 6. If the three sides of a right triangle are continuous even numbers, its circumference is _ _ _ _.

Second, multiple-choice questions (4 points for each question, counting 20 points) 1, at Rt△ABC, ∠C=90, the circumference is 60, and the ratio of the hypotenuse to a right-angled side is 13: 5, then the three sides of this triangle are () A, 5, 4, 3 respectively; b、 13、 12、5； c、 10、8、6； D, 26, 24, 10 2, the length of the following three groups of line segments 19, 12,15; ②7、24、25; ③32、42、52; ④3a、4a、5a(a & gt； 0); ⑤m2-n2, 2mn, m2 n2(m, n is a positive integer, m >；; N) There are () a and 5 groups that can form a right triangle; Group b and group 4; Group c and group 3; D, Group 2, Group 3: Fold a triangle with three sides BC=3, AC=4 and AB=5 along the longest side AB on the same plane to get △ABC', then the length of CC' is equal to () a,; B, yes; C, yes; D, 4, the following conclusions are wrong: (a) A triangle with the ratio of three angles of 1: 2: 3 is a right triangle; B, the triangle with the ratio of three sides length of 3: 4: 5 is a right triangle; C, the triangle with the ratio of three sides of 8∶ 16∶ 17 is a right triangle; D A triangle whose ratio of three angles is 1: 1: 2 is a right triangle. 5. One side of a right triangle is 1 1, and the other two sides are also positive integers, so the perimeter of this triangle is () a,120; b、 12 1； c、 132； d、 123

1. It is known that x and y are positive numbers and │x2-4│ (y2-3)2=0. If you make a right triangle with the length of X and Y, the area of the square with the hypotenuse as the side length of this right triangle is ().

a，5 B，25 C，7 D， 15 2。 In △ABC, point D is the midpoint of BC, BD=3, AD=4, AB=5, then AC = _ _ _ _ _ _ _ _ 3. In △ABC, AB=2k, AC=2k- 1, BC=3, and when K = _ _ _ _ _ _ _ _ C = 90. 4. It is known that the three sides of a right triangle are 6, 8 and x respectively, and the area of a square with x as the side length is _ _ _ _ _. 5. Given that the hypotenuse length of a right triangle is 12㎝ and the perimeter is 30㎝, the area of the triangle is _ _ _ _. 8. Bend a wire with a length of 10㎝ into two right-angled sides of a right-angled triangle. If the area of the triangle is 9㎝2, then a wire with a length of _ _ _ must be prepared to make the triangle well. 1. Multiple choice questions 1. At Rt△ABC, ∠ c = 90, and the lengths of the three sides are A, B and C respectively, the following conclusions remain unchanged: () A, 2AB.

2. It is known that x and y are positive numbers and │x2-4│ (y2-3)2=0. If you make a right triangle with the sides of X and Y, then the area of the square with the hypotenuse of this right triangle as the side is () a, 5 B, 25 C, 7 D, 15.

3. The length of a right triangle is 12, and the lengths of the other two sides are natural numbers, so there are () a, 4 B, 5 C, 6 D, and eight right triangles that meet the requirements.

4. The following propositions ① If A, B and C are a set of pythagorean numbers, then 4a, 4b and 4c are still pythagorean numbers; ② If both sides of a right triangle are 3 and 4, then the hypotenuse must be 5; ③ If the three sides of a triangle are12,25 and 2 1 respectively, then the triangle must be a right triangle; ④ The three sides of an isosceles right triangle are A, B, C, (A >；; B=c), then a2∶b2∶c2=2∶ 1∶ 1. The correct ones are () a, 12B, 13C, 14D, 2④.

5. If the three sides A, B and C of △ABC satisfy a2 b2 c2 338= 10a 24b 26c, then △ is () A, acute triangle B, obtuse triangle C and right triangle D, which cannot be determined.

6. It is known that the waist length of an isosceles triangle is 10, and the height of one waist is 6, so the area of a square with the bottom as the side length is () a, 40 B, 80 C, 40 or 360 D, 80 or 360.

9. An ant climbs from point A to point B of a rectangular box with a length and width of 3 and a height of 8, so the length of the shortest route it takes is _ _ _ _ _ _ _ _. 10. On the calm lake surface, there is a red lotus, which is 1 m higher than the water surface. A gust of wind blew, and the red-violet was blown aside, and the flowers were flush with the water. It is known that the horizontal distance of red-violet movement is 2 meters, and the water depth here is _ _ _ _ _ _ _.

27.(8 points) It is known that in △ABC, AB = 17 cm, BC = 16 cm, and the center line of BC side = 15 cm. Explain that △ABC is an isosceles triangle.

1. Given that both sides of an Rt△ are 3 and 4 respectively, the square of the third side is () a, 25 B, 14 C, 7 D, 7 or 25 2. In the following groups, the triangle with sides A, B and C is not Rt△ and () A, A = 65438. C= 10 D，a=3，b=4，c=5 3。 If line segments A, B and C form Rt△, their ratios are () A, 2∶3∶4 B, 3∶4∶6 C, 5 ∶ 12 ∶ 12. Then the circumference of Rt△ is () a, 12 1 B, 120 C, 132 D, which is uncertain. 5. If the ratio of two right angles of Rt△ is 5∶ 12, the ratio of the height on the hypotenuse to the hypotenuse is () a, 60∶ 13 B, 5∶ 12 C, 12∶ 13 D, 66. If the two right angles of Rt△ are N2-65438+ respectively. 1), then its hypotenuse length is () a, 2n B, n 1 C, n2- 1 D, n2 1 7. It is known that Rt△ABC, ∠ c = 90, and if AB = 14 cm, the area of Rt△ABC is () a, 24cm2 B, 36cm2 C, 48 Cm2 D and 60cm2 8. If the height on the base of an isosceles triangle is 8 and the circumference is 32, then the area of the triangle is () a, 56 B, 48c, 40 D, 32 9. The length of three sides of a triangle is (a b)2=c2 2ab.

A. equilateral triangle; B. obtuse triangle; C. right triangle; D. acute triangle

13. in Rt△ABC, ∠ c = 90; (1) if A = 5, B = 12, then C = _ _ _ _ _ _ _ _ _ _ _ _ _； (2) if a = 15 and c = 25, then b = _ _ _ _ _ _ ③ If c = 6 1 and b = 60, then a = _ _ _ _ _ _ ④ If a: b = 3: 4, c. 15. The lengths of two right angles of a right triangle are 5 and 12 respectively, so the height on its hypotenuse is _ _ _ _ _ _ _. 16. On the calm lake surface, there is a red lotus, which is 1 m higher than the water surface. A gust of wind blew, and the red-violet was blown aside, and the flowers were flush with the water. It is known that the horizontal distance of red-violet is 2m, and the water depth here is _ _ _ _ _ _. 17. It is known that the lengths of the two line segments are 5cm and 12cm respectively. When the length of the third line segment is cm, these three line segments can form a right triangle.