Right triangle properties, what are the properties of right triangles

MEF is an isosceles right triangle, reason: auxiliary line: connect AM, from the meaning of the title, we know that BF=DF=AE, AM=BM, B= MAE, BMF is all equal to AME, so MF=ME, BMF= AME, FME=90°, FMEs are isosceles right triangles.

Let's take a picture with a clear point, I can't see it clearly.

The properties are described below:

Two acute angles of a right triangle are interdependent; The middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse; In a right-angled triangle, the right-angled side of the 30-degree angle is half the hypotenuse; In a right-angled triangle, if there is a right-angled edge equal to half of the hypotenuse, then the sharp angle of the right-angled edge is equal to 30°.

A right triangle is a geometric figure, which is a triangle with a right angle angle, and there are two types: ordinary right triangle and isosceles right triangle.

Solution: The properties of a right triangle are: the middle line on the hypotenuse is equal to half of the hypotenuse; Two acute angles are redundant; The sum of the squares of the two right-angled sides is equal to the square of the hypotenuse; The square of the hypotenuse minus the square of the straight corner is equal to the square of the other right angle; The area is 1/2 of the product of the two right-angled edges = 1/2 of the product of the hypotenuse and the height of the hypotenuse (quadratic); When there is an angle of 45°, the two hypotenuses are equal; When there is an angle of 30°, the side opposite by the 30° angle is half of the hypotenuse; In the RT triangle ABC, at the angle A=90°, sinb=cosc=ac:

bc,tanb(c)=b(c)sin b(c)cos(this is a trigonometric culvert number and there is a lot of knowledge);

1.The two acute angles are surplus 2The sum of the squares of the two right-angled sides = the square of the third side, a + b = c (Pythagorean theorem) 3

The middle line on the hypotenuse = half of the hypotenuse 4The area of the triangle = half of the two right-angled sides of the plane5If the height length on the hypotenuse is h, then a*b=c*h 6

Projective theorem 7If there is an acute angle of 30 degrees, then the right-angled edge opposite the angle is half of the hypotenuse. Beg!!!

1.Two acute angles are redundant;

2.The sum of the squares of the two right-angled sides is equal to the square of the hypotenuse, a + b = c (Pythagorean theorem) 3The midline on the hypotenuse = half of the hypotenuse.

The edge corresponding to the angle of degrees is equal to half of the hypotenuse.

1. The Pythagorean theorem The edge corresponding to the degree angle is equal to half of the hypotenuse ......Some forgot.

1 Pythagorean theorem 2 The side of 30 degrees is half of the hypotenuse 3 The middle line on the hypotenuse is equal to half of the hypotenuse, and the triangle enclosed by the angle of the side is an equilateral triangle.

Right triangles have the following 10 properties:

1. The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

2. In a right-angled triangle, two acute angles are redundant.

3. In a right-angled triangle, the middle line on the hypotenuse is equal to half of the hypotenuse (i.e., the outer center of the right-angled triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle r c 2).

4. The product of the two right-angled sides of a right-angled triangle is equal to the product of the hypotenuse and the height of the hypotenuse, that is, ab=ch.

5. The vertical center of the right triangle is located at the vertex of the right angle.

6. The radius of the inscribed circle cover of the right-angled triangle is equal to half of the difference between the sum of the two right-angled edges minus the hypotenuse, that is, r a+b-c 2.

7. In a right-angled triangle, the height on the hypotenuse is the projective ratio of the two right-angled sides on the hypotenuse.

8. In a right-angled triangle, each right-angled side is the projective and hypotenuse of the right-angled edge on the hypotenuse Proportion of the hypotenuse Thus, the square ratio of the two right-angled sides of the right-angled triangle is equal to their projective ratio on the hypotenuse.

9. The ratio of the three sides of a right-angled triangle containing 30° is 1:3:2.

10. The ratio of the three sides of a right triangle with a 45° angle is 1:1: root number 2.

Property 1: The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse

Property 2: In a right triangle, two acute angles are surplus to each other

Property 3: In a right triangle, the midline on the hypotenuse is equal to half of the hypotenuse (i.e., the center of the right triangle is located at the midpoint of the hypotenuse, and the circumscribed radius r c 2).

Property 4: The product of the two right-angled sides of a right-angled triangle is equal to the product of the hypotenuse and the height of the hypotenuse, i.e., ab=ch

Property 5: The vertical center of a right triangle is located at the vertex of the right angle

Property 6: The radius of the inscribed circle of a right triangle is equal to half of the sum of the two right angles minus the difference between the hypotenuses, i.e., r a+b-c 2

Property 7: In a right triangle, the height on the hypotenuse is the projective ratio of the two right sides on the hypotenuse

Property 8: In a right triangle, each right angle side is the projective and hypotenuse of the right angle on the hypotenuse Proportional term Thus, the square ratio of the two right sides of a right triangle is equal to their projective ratio on the hypotenuse

Property 9: The ratio of the three sides of a right triangle containing 30° is 1: 3:2

Property 10: The ratio of the three sides of a right triangle with an angle of 45° is 1:1:2

1. The difference between any two sides is less than the third beat of the macro side.

2. The sum of any two sides is greater than the third side.

3. The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

4. In a right-angled triangle, the middle line on the hypotenuse is equal to half of the hypotenuse.

5. The product of the two right-angled sides of a right-angled triangle is equal to the product of the hypotenuse and the height of the hypotenuse.

6. The ratio of the three sides of an isosceles right triangle is 1:1: root number two.

The property of a right-angled triangle with a 30-degree angle is that the length of the right-angled side corresponding to the 30° angle is half the length of the hypotenuse.

The ratio of the three sides of a 30-degree right-angled triangle is 1: 3: the right-angled triangle of degrees is a special right-angled triangle, and its three angles are 30 degrees, 60 degrees and 90 degrees, according to the sine theorem of the triangle, it can be known that the corresponding sinusoidal function value of the triangle angle is equal to the ratio of the corresponding sides, that is, the spring beat:

sin30：sin60：sin90=1：

Right triangle

An isosceles right triangle is a special type of triangle that has all the properties of a triangle: with stability, an inner angle and a forest sky of 180°. The two right-angled sides are equal, the two acute angles are 45°, the middle line, the angle bisector and the perpendicular line on the hypotenuse are one, and the height on the hypotenuse of the isosceles right-angled triangle is the radius r of the circumscribed circle of the triangle.

The sum of the three internal angles of the triangle is equal to 180°. One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it. One outer corner of a triangle is larger than any of the inner angles that are not adjacent to it.

The sum of the two sides of the triangle is greater than the third side, and the difference between the two sides is less than the third side. Within the same triangle, the big side is against the big angle, and the big angle is against the big side.

The above content reference:Encyclopedia – Right Triangle