1. In △ABC, ∞∠C = 90. (1+0) If A = 2 and B = 3, what is the area of a square with C as its side? (2) If A = 5 and C = 13, what is B? (3) If c = 6 1 and b = 1 1, what is a? (4) If a∶c =3∶5 and c =20, what is B? (5) If ∠ A = 60 and AC =7cm, AB = _cm and BC = _cm.
2. A right side and hypotenuse of a right triangle are 8cm and 10cm respectively, so the height on the hypotenuse is higher than _ cm.
3. The circumference of an isosceles triangle is 20cm, the base height is 6cm and the base length is _ cm.
4. In △ABC, if AD = _cm, ∠ BAC = 120, AB = 12 cm, the height of BC is _cm.
5. When △ABC, ∠ ACB = 90, CD⊥AB is in D, BC=, DB=2cm, then BC = _ BC=_ cm, AB= _cm, AC= _cm _ cm.
6. As the picture shows, someone has thought about crossing the river. Due to the influence of ocean current, the actual landing point C deviates from the scheduled arrival point B200m. As a result, he actually swam 520m in the water, and the width of the river was _ _ _ _ _.
7. There are two monkeys at the height of 10 meter of a tree. A monkey climbed down the tree and walked to the pond 20 meters away from the tree. The other climbs to the top of the tree D and jumps directly to A, and the distance is calculated in a straight line. If two monkeys pass the same distance, the tree is _ _ _ _ _ _ _ meters high.
8. Given an Rt△, the two sides are 3 and 4 respectively, and the square of the third side is ().
A, 25 B, 14 C, 7 D, 7 or 25
Xiaofeng's mother bought a 29-inch (74 cm) TV set. Which of the following statements about 29 inches is correct?
A. Xiaofeng thinks it refers to the length of the screen; B. Xiaofeng's mother thinks it refers to the width of the screen;
C. Xiaofeng's father thinks it refers to the circumference of the screen; D. Salesman thinks it refers to the diagonal length of the screen.
2. How many ways do you prove that a triangle is a right triangle?
Exercise:
(× classic exercises ×)
According to China's ancient "Zhou Kuai Shu Jing", Shang Gao told the Duke of Zhou in 1 120 BC that if a ruler is folded into a right angle, the two ends are connected to form a right triangle. If the hook is three and the strand is four, then the string is equal to five, which is summarized as "hook three, strand four and string five" by later generations.
(1) Observation: 3, 4, 5, 5, 12, 13, 7, 24, 25, ... It is found that the ticks of these groups are all odd, and they have not stopped since 3. Calculate 0.5 (9+ 1) and 0.5 (25- 1) and 0.5 (25+ 1), and write the formulas of strands and chords that can represent the three numbers of 7, 24 and 25 respectively according to the rules you found.
(2) According to (1) law, if all these pythagorean strands are represented by n(n is odd, n≥3), please directly represent their chords by algebraic expressions containing n..
Answer:
( 1) 0.5(9+ 1)∧2+0.5(25- 1)∧2= 169=0.5(25+ 1)∧2 0.5( 13+ 1)∧2+0.5(49- 1)∧2=0.5(49+ 1)∧2
(2) Chord: 0.5 (n 2- 1) Chord: 0.5 (n 2+ 1)
If the three sides of a triangle are (a+b)2=c2+2ab, then the triangle is ().
A. equilateral triangle; B. obtuse triangle; C. right triangle; D. acute triangle
1. in Δ Δ ABC, if AB2+BC2 = AC2, then ∠ A+∠ C = 0.
2. As shown in the figure, if the side length of a small square is 1, the △ABC in the square grid is ().
(a) right triangle (b) acute triangle
(c) obtuse triangle (d) None of the above answers are correct
Given that the lengths of three sides of a triangle are 2n+ 1, 2n+2n, 2n+2n+ 1 (n is a positive integer), the maximum angle is equal to _ _ _ _ _ _ _.
The degree ratio of the three internal angles of a triangle is 1:2:3, and its largest side is m, so its smallest side is _ _ _ _.
The area of an isosceles right triangle with the hypotenuse height of m is equal to _ _ _ _.
3. As shown in the figure, in quadrilateral ABCD, AB=3cm, AD=4cm, BC= 13cm, CD= 12cm, ∠ A = 90, find the area of quadrilateral ABCD.