Triangle math problems, you can t use the Pythagorean theorem

CE perpendicular AF, along the CE folded triangle AEC, crossed AF to M to obtain AC=MC from AC=BC to BC=MC

If the BM is connected, the BM and AM are of equal length.

The intersection point of AB and CE is n

Then the triangle AEN is similar to the triangle AFB

then ae:af=an:ab=1:4

Gain ae = 2

bm=am=2√2

It doesn't feel right, I haven't done it for a long time, you refer to it.

AC=BC=cm, take the midpoint n of BM, and connect CN, so the angle BCN=1 2 angle BCM

Angle BAF = 90 degrees - angle cab - angle ACE = 90 degrees - (180 degrees - angle ACB) 2-angle ACE = angle BCM 2 = angle BCN

CE is parallel to BF, CE and AB intersect at point D, angle ABF = 90 degrees - angle BAF = angle CDB = angle CAB, angle ACD is equal to 0, so D is point A, so C, D (A), E three points are collinear, that is, E is point A, M is point A, sin angle ACB = AF BC=3 10 10, so BM = BA = 2BC * SIN (angle ACB 2) = 2 * (10- 10).

AC=BC, angle AFB=90 degrees, CE perpendicular AF, along the CE folded triangle AEC, cross AF at M, cross the point B to make the perpendicular line of CM, BC=2 times the root number 5, EF=3 times the root number 2, find BM

CE perpendicular AF, along the CE folded triangle AEC, crossed AF to M to obtain AC=MC from AC=BC to BC=MC

If the BM is connected, the BM and AM are of equal length.

The intersection point of AB and CE is n

Then the triangle AEN is similar to the triangle AFB

then ae:af=an:ab=1:4

Gain ae = 2

bm=am=2√2

Damn, your drawings are too high-level, and people can't afford to worship them.

According to the Pythagorean theorem, if the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a2+b 2=c 2;; That is, the sum of the squares of the right-angled sides of the right-angled triangle is equal to the square of the hypotenuse length.

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. It conforms to the Pythagorean theorem and has some special properties and judgment methods.

Solve with trigonometric functions. Know the opposite edge and adjacent edge, tan = opposite edge adjacent edge, and then use the calculator to find the angle.

Knowing the opposite side and the hypotenuse, sin = the opposite side of the hypotenuse, then use the calculator to find the angle.

Knowing the adjacent edge and the hypotenuse, cos = adjacent edge hypotenuse, and then use the calculator to find the angle.

1. The Pythagorean theorem calculates the length of the other side: c 2 = a 2 + b 2 a, b is the right-angled edge, c is the hypotenuse.

2. The opposite side of the answer of sina = a: the hypotenuse of a, according to the value of sin to get the degree.

In the same way, there is cosa = margin: hypotenuse; tana=opposite: border; cota = marginal: opposite edge.

Special natureIn addition to its general triangular nature, it has some special properties:

3. In a right-angled triangle, the middle line on 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 is known as the hypotenuse midline theorem of a right triangle.

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

This is the problem of the proportion of the Pythagorean theorem of the Pythagorean Hypothem, the angle of 30 degrees is a special angle, so the opposite side of 30 degrees is half of the hypotenuse, this is a basic common sense, according to the Pythagorean theorem, we can get the shortest right-angled side is a, the other right-angled side is 3a, and the hypotenuse is 2a, then this is the proportional relationship of their three sides, 1: 3:2.

Pythagorean theorem formula.

1. Basic formula.

In a right-angled triangle on a plane, the square of the lengths of the two right-angled sides adds up to the square of the hypotenuse lengths. If the length of the two right-angled sides of the right-angled triangle is a and b, and the length of the hypotenuse is c, then the formula of the Pythagorean theorem is a 2 + b 2 = c 2.

2. Complete formula.

a=m,b=(m k-k) 2,c=(m k+k) 2 where m 3

1) When m is determined to be an odd number of any 3, k = {1, all factors of m less than m}

2) When m is determined to be an even number of any 4, k = {m 2 is all smaller than the even factor of m}

3. Common formulas.

1）（3,4,5),(6,8,10)……3n, 4n, 5n (n is a positive integer).

2）（5,12,13),(7,24,25),(9,40,41)……2n+1, 2n+2n, 2n+2n+1 (n is a positive integer and missing key).

3）（8,15,17),(12,35,37)……2*(n+1), -1, +1 (n is a positive integer).

4) m-n, 2mn, m+n (m and n are both positive integers, m>n).

The Pythagorean theorem only applies to right triangles.

The Pythagorean theorem is a fundamental geometric theorem that states that 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 ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, the other long right-angled side was the strand, and the hypotenuse was the chord, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

Yes. The Pythagorean theorem is specific to direct triangles. Hook three strands, four strings, five.

The Pythagorean theorem can be used for right triangles, so please learn the Pythagorean theorem as soon as possible.

Oh, yes? When the two lines of the hook (q), strand (p), chord (s), and the meeting point are at an angle of 90 degrees, the power formula is calculated: s p q, s p q. p s a q , q s p

The Pythagorean theorem can be applied: hypotenuse square = sum of squares of two right-angled sides. The sedan shouted

For example, for any long-angle triangle, if the length of the two right-angled sides is a and b, and the length of the hypotenuse is c, then the formula can be obtained according to the Pythagorean theorem: a +b = c.

For example, two sides are one and one long, and the Pythagorean theorem can be obtained: hypotenuse = (.

Discovery of the Pythagorean theorem.

The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and one of the links between numbers and shapes.

In China, Shang Gao during the Zhou Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean three, four strings, five". In the West, the Pythagoreans of ancient Greece were the first to propose and prove this theorem in the 6th century BC, who used the deductive method to prove that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the squares of two right-angled sails.

Yes. Because this is the definition of the Pythagorean theorem: the Pythagorean theorem is a basic elementary geometric theorem that states that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

If the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c, and if a, b, and c are all positive integers, (a, b, c) is called the Pythagorean array.

The Pythagorean theorem now has about 500 ways to prove it, making it one of the most provable theorems in mathematics. The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and one of the links between numbers and shapes.