As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4, the vertical bisector De of AB intersects the extension of BC at point E, then the length of CE is () A. 3 Two B. 7 Six C. 25 Six D. 2

As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4, the vertical bisector De of AB intersects the extension of BC at point E, then the length of CE is () A. 3 Two B. 7 Six C. 25 Six D. 2

∵∠ACB=90°，BC=3，AC=4，
According to Pythagorean theorem, ab = 5,
The vertical bisector De of AB intersects the extension of BC at point E,
∴∠BDE=90°，∠B=∠B，
∴△ACB∽△EDB，
/ / BC: BD = AB: (BC + CE), and BC = 3, AC = 4, ab = 5,
∴3：2.5=5：（3+CE），
Thus, CE = 7
6．
Therefore, B

As shown in the figure, in △ ABC, ∠ C = 90 ° the vertical bisector of AB intersects BC at D, ∠ CAD: ∠ DBA = 1:2, then the degree of ∠ DBA is______ .

∵ de bisects AB vertically,
∴∠DBA=∠BAD，
∵∠CAD：∠DBA=1：2，
ν if ∠ DBA = 2x, then ∠ bad = 2x, ∠ CAD = x,
∴x+2x+2x=90°，
∴x=18°，
∴∠DBA=2x=2×18°=36°．

As shown in the figure, in the right triangle ABC, the angle c is equal to 90 degrees, BC = 10, AC = 6, and De is the perpendicular line of ab. find the length of CE and be

If e is on the edge of AB or on the edge of BC, then the steps are as follows: connect AE because De is the vertical line of AB, so AE = be, and because CE + be = BC = 10, AE + CE = 10. If CE is set to x, then AE is 10-x, x? + AC? = (10-x) 2, x = 3.2 be = bc-ce = 10-3.2 = 6.4

Proof: the center line on the hypotenuse of a right triangle is equal to half of the hypotenuse

It is known that in △ ABC, ∠ ACB = 90 ° and CD is the center line on the hypotenuse ab,
Confirmation: CD = 1
2AB；
Proof: as shown in the figure, extend CD to e, make de = CD, connect AE and be,
∵ CD is the center line on the hypotenuse ab,
∴AD=BD，
The aebc is a parallelogram,
∵∠ACB=90°，
The quadrilateral aebc is a rectangle,
∴AD=BD=CD=DE，
∴CD=1
2AB．

The central line on the hypotenuse of a right triangle is equal to half of the hypotenuse!

Method 1:
Δ ABC is a right triangle, which is the vertical bisector of AB and intersects BC with D
/ / ad = BD (the distance from the point on the vertical bisector of the line segment to the two ends of the line segment is equal)
Draw an arc with DB as the radius and D as the center of the circle, and intersect with BC on the other side of D at C '
 DC '= ad = BD  bad = ∠ abd ∠ c'ad = ∠ ac'd (equilateral and equal angle)
And ? bad +  abd +  c'ad + ∠ ac'd = 180 ° (sum theorem of interior angles of triangles)
Ψ bad + ∠ c'ad = 90 ° i.e. ∠ BAC '= 90 °
And ∵ BAC = 90 
∴∠BAC=∠BAC’
⊥ AB, c'a ⊥ AB, so there are two straight lines Ca and c'a that are perpendicular to ab through a, which contradicts the vertical axiom  hypothesis does not hold  C and C 'coincide)
 DC = ad = BD  ad is the median line on BC and ad = BC / 2. This is the central line theorem on the hypotenuse of a right triangle
Method 2:
Δ ABC is a right triangle, ad is the center line of BC, and is the midpoint e of AB, connecting De
ν BD = CB / 2, De is the median line of Δ ABC
▽ de ‖ AC (the median line of the triangle is parallel to the third side)
﹤ DEB = ∠ cab = 90 ° (two lines are parallel and the same position angle is equal)
∴DE⊥AB
Ψ e is the vertical bisector of ab
/ / ad = BD (the distance from the point on the vertical bisector of the line segment to the two ends of the line segment is equal)
∴AD=CB/2

Area of right triangle in Pythagorean theorem

Pythagorean Theorem A ^ 2 + B ^ 2 = C ^ 2, base times height divided by two

To draw a right triangle, the ratio of the two acute angles should be 1:2 Main formula

The angle of the long side pair is 60 degrees and that of the short side pair is 30 degrees

The ratio of the two acute angles of a right triangle is 2:1. What are the two acute angles

Let two acute angle degrees be x and Y respectively
Then x + y + 90 = 180
x/y=2:1
By solving the equations, x = 60, y = 30

A long right angle side of a right triangle is 7.5, and its corresponding angle is 75 degrees. Find out the length of its other right angle side and oblique side

Length of the other right angle side = 7.5 (2 - √ 3)
Slant side length = 15 √ (2 - √ 3)
After questioning

How long is the hypotenuse of a right triangle?

thirty-one point seven six
The square sum of two simple square root