Linear equations for triangular sides? 20

The vertex of the isosceles triangle is (3,-4) and the equation of the line where the hypotenuse is 3x+4y=12, find the equation of the line where the two right-angled sides are located.

3x+4y=12 gives y=-3x 4+3, and the slope of the straight line where the hypotenuse is located is -3 4

Let the inclination angle of the line where the hypotenuse is located be

Then the inclination angle of the line on which one right-angled edge is located is +4, and the inclination angle of the line on which the other right-angled edge is located is -4

tan(θ+/4)=[tanθ+tan(π/4)]/[1-tanθtan(π/4)]

tan(θ-/4)=[tanθ-tan(π/4)]/[1+tanθtan(π/4)]

The slopes of the two right-angled edges are 1 7 and -7, respectively, and the points are (3, -4).

Let the equations for the straight line where the two right-angled edges are located y=x 7+m and y=-7x+n, respectively

Substitution point (3,-4).

3 1 7 + m = -4 to get m = -31 7

3 (-7)+n=-4 gives n=17

The equations for the straight line on which the two right-angled edges are located are y=x7-31 7 and y=-7x+17, respectively

It is faster to use two-point or point-oblique type.

You need to have coordinates for three vertices (x1, y1), (x2, y2), (x3, y3).

Then according to the formula to find the straight line equation, let the straight line equation as y=a+bx, and substitute the above coordinates into this equation, you can calculate the straight line equation of the edge.

y=[y1-x1(y2-y1)/(x2-x1)]+y2-y1)/(x2-x1)x

y=[y2-x2(y3-y2)/(x3-x2)]+y3-y2)/(x3-x2)x

y=[y1-x1(y3-y1)/(x3-x1)]+y3-y1)/(x3-x1)x

Right triangleBeveled edgesThe midline is equal to half the width of the hypotenuse.

A right triangle is a geometric figure, which is a triangle with an angle at right angles, and there are ordinary right triangles and isosceles right triangles.

Both. It conforms to the Pythagorean theorem.

It has some special properties and judgment methods.

The length of the midline on the hypotenuse of a right triangle is half the length of the hypotenuse.

2) The midpoint is at an equal distance from the three vertices of the right triangle. Reading is bright.

3) Divide the right triangle into 2 triangles of equal area. The three middle lines of any triangle divide the triangle into six equal parts. The middle line divides the triangle into two parts of equal area.

The hypotenuse midline theorem of a right triangle is a very stupid theorem about right triangles in mathematics.

Specifically, if a triangle is a right triangle, then the middle line on the hypotenuse of the triangle is equal to half of the hypotenuse.

The center line of the triangle is divided into equal areas of the triangle, the three center lines of the triangle intersect at one point, which is called the center of gravity of the triangle, and the center line on the hypotenuse of the right triangle is equal to half of the hypotenuse.

The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse; In a right-angled triangle, two acute angles are surplus to each other, and the midline on the hypotenuse is equal to half of the hypotenuse, a property called the hypotenuse midline theorem of the right-angled triangle; The product of the two right-angled sides of a right-angled triangle is equal to the product of the oblique side and the height of the hypotenuse; In a right-angled triangle, if there is an acute angle equal to 30°, then the right-angled side it is facing is equal to half of the hypotenuse; The two right triangles that are divided by the high division on the hypotenuse are similar to the original triangles.

But Qi Ye uses the Pythagorean theorem to calculate: if the length of the two right-angled sides of a right-angled triangle is a, b, and the length of the hypotenuse is c, then a +b = c.

Analysis: The Pythagorean theorem is satisfied in a right triangle – in a right triangle on a plane, the square of the side lengths of the two right sides adds up to the square of the hypotenuse lengths. Mathematical expression: a + b = c

A +b =c to find c, because c is an edge, so it is to find a root greater than 0. i.e. c= (a +b).

Solution: Let the length of one right-angled side of a right-angled triangle be b, and the angle of this side is t, and the length of the other two sides can be obtained by using trigonometric functions

1) The length of the other right-angled edge ab c=b tant;

2) The length of the hypotenuse cb a=b sint.

1. Opposite side. The line on the opposite side of this corner.

2. Adjacent edges. The neighbors of this corner, the two lines that make up this corner.

3. Hypotenuse. The longest of the three lines of a right triangle.

Determination of right triangles.

1. A triangle with an angle of 90° is a right triangle.

2. If the square of a + the square of b = the square of c, then the triangle with a, b, and c as the sides is a right triangle with c as the hypotenuse (the inverse theorem of the Pythagorean theorem).

3. If the side of a triangle is half of a certain side at the 30° inner angle, then the triangle is a right-angled triangle with the long side as the hypotenuse.

4. A triangle with two acute angles remaining with each other is a right-angled triangle.

5. When proving the congruence of right triangles, you can use HL, the hypotenuse lengths of the two triangles correspond to the same, and the brother fiber and a right angle side correspond to the equal, then the two right triangles are congruent.

6. If two straight lines intersect and the product of their slopes is negative to each other, then the two straight lines are perpendicular.

7. In a triangle, if the middle line on one side of it is equal to half of the side where the middle line of the lead base is located, then the triangle is a right triangle.

In a planar graphic, a straight line is a polygon with straight sides on each side.

A closed figure consisting of three line segments that are not on the same straight line is connected one after the other, which is called a triangle.

The figure enclosed by three straight lines on the plane or three arcs on the sphere, and the figure enclosed by the three straight lines is called a plane triangle; The shape enclosed by three arcs is called a spherical triangle, also known as a trilateral.

The closed geometry obtained by connecting the three line segments end to end is called a triangle, and the triangle is the basic shape of the geometric pattern.