How to judge a right triangle, how to tell if it is a right triangle?

Determination of right triangles:

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

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

Judgment 3: If the side of a triangle within 30° is half of one side, then the triangle is a right triangle with the long side as the hypotenuse.

Judgment 4: A triangle with two acute angles remaining with each other is a right triangle.

Judgment 5: When proving the congruence of a right triangle, it is possible to use hl, where the hypotenuse of two triangles corresponds to the same length, and one right angle side corresponds to the same, then the two right triangles are congruence. (Theorem:.)

The hypotenuse and a right angle correspond to two equal right triangle congruences. Abbreviated as HL).

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

Judgment 7: In a triangle, if the middle line on its hypotenuse is equal to half of the hypotenuse, then the triangle is a right triangle.

1:2:3 is a right-angled triangle.

Because 1 + (3) = 2, it is a right triangle, and because 1 2 = 2, so according to the right angle side is half of the hypotenuse half of the right triangle opposite side is 30, it can be seen that this is a right triangle with 30 angles.

Solution: Let the three sides be a, 2a, 3a, then (2a) 2=a 2+( 3a) 2, so the triangle is a right triangle.

According to the big angle to the big side, the hypotenuse is 2a, because a 2a = 1 2 so the smaller angle is 30°, so the other angle is 60°.

The nature of a right triangle

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

2. In a right-angled triangle, the middle line of the hypotenuse is equal to half of the hypotenuse (that is, 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). This property of the pietrousers is called the right-angled triangle hypotenuse midline theorem.

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

4. In a right-angled triangle, if there is an acute angle equal to 30°, then the right-angled side it is opposite is equal to half of the hypotenuse.

5. The two right triangles of a right triangle are similar to the original triangle by the high division on the hypotenuse.

First, the right triangle determination method:

Judgment 1: Definition, a triangle with an angle of 90° is a right triangle.

Judgment 2: Judgment theorem: A triangle with a, b, and c as the sides is a right triangle with c as the hypotenuse.

If the three sides of the triangle and or a,b,c satisfy a 2+b 2=c 2, then the triangle is a right triangle. (The inverse theorem of the Pythagorean theorem).

Judgment 3: If the side of a triangle within 30° is half of one side, then the triangle is a right-angled triangle with the long side as the hypotenuse.

Judgment 4: A triangle in which two acute angles are co-angles to each other (the sum of the two angles equals 90°) is a right triangle. Judgment 5: If two straight lines intersect and the product of their slopes is negative to each other, then the two lines are perpendicular to each other. So.

Judgment 6: If the median line on one side of a triangle is equal to half of its side, then the triangle is a right triangle.

Judgment 7: If the opposite side of a triangle at an angle of 30° is equal to half of the hypotenuse of the triangle, then the triangle is a right triangle. (Unlike Decision 3, this theorem is used for triangles with known hypotenuse.) ）

2. Definition of right triangle:

There is a triangle with an angle of 90° called a right triangle. A right triangle can be represented by RT, such as a right triangle ABC written as RT ABC.

The determination of a right triangle can be based on two aspects: definition and nature.

1. Definition of right triangle:

There is a triangle with an angle of 90°, which is called a right triangle. A right triangle can be represented by RT, such as a right triangle ABC written as RT ABC.

2. Right triangle properties:

1. The nature of the angle: the two acute angles of the right triangle are mutually reinforcing, which is relatively simple.

2. The nature of the edge: the three sides of the right triangle satisfy the Pythagorean theorem, which is the most important property of the right triangle.

3. The height on the hypotenuse: the product of the hypotenuse of the right triangle is higher than the product of the two right-angled sides divided by the hypotenuse, or this is a very common method for us to find the high line.

4. The middle line on the hypotenuse: the middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse, which is commonly used in geometric calculations and proofs, and is easy to be ignored.