The property that the sum of squares of two right angles of a triangle is equal to the square of the hypotenuse is called Pythagorean theorem or Pythagorean theorem. Mathematical formulas are often written as a 2+b 2 = c 2. 3 2+4 2 = 5 2, so it is a right angle.

The answer process is as follows:

(1) This question examines the solution of the area of a right triangle. There are two solutions to the area of a right triangle, and the two solutions are the same for the same right triangle.

(2) In the first solution, half of the product of two right angles is the area of a triangle, and the mathematical expression is: 1/2×3×4.

(3) In the second solution, half of the product of the hypotenuse and the height on the hypotenuse is the area of the triangle, and the mathematical expression is:1/2× 5× h.

(4)1/2× 3× 4 =1/2× 5× h, and the solution is H = 12/5cm. 12/5=2.4 cm.

Determination of right triangle;

1. If the opposite side of the 30 internal angle of a triangle is half of one side, the triangle is a right triangle with this long side as the hypotenuse.

2. A triangle whose two acute angles are complementary (the sum of the two angles is equal to 90) is a right triangle.

3. If two straight lines intersect and the product of their slopes is negative reciprocal, then the two straight lines are perpendicular to each other. Then this triangle is a right triangle.

If the median line of one side of a triangle is equal to half of its side, then this triangle is a right triangle. Refer to the right triangle hypotenuse midline theorem.

If the opposite side of a triangle is equal to half of the adjacent side, then the triangle is a right triangle.