It is known that in △ ABC, points D, e and F are points on BC, AB and AC respectively, AF is parallel to ED, and AF = ed, extend FD to point G, so that DG = FD, and verify that ED and Ag are equally divided,

Because AF and ED are parallel and equal, the quad AEDF is a parallelogram
So AE and FD are parallel and equal because DG = FD
So AE and DG are parallel and equal
So the quadrilateral aegd is a parallelogram
So Ed and Ag share equally

In the triangle ABC, a = 90, ab = AC, D is the midpoint of BC, be = AF, ed = FD

In triangle ABC, angle a = 90, ab = AC, which means that triangle is isosceles right triangle
D is the midpoint of BC, which indicates that ad is the vertical line of isosceles right triangle, and that abd and ACD are isosceles right triangles
It is easy to know that angle abd = angle DAC = 45 degrees;
It is also easy to know that BD = ad
And because be = AF
So triangle bed and triangle AFD are congruent triangles
So Ed = FD
It's over

In △ ABC, ab = AC, ∠ BAC = 90 °, D is the midpoint of BC, ed ⊥ FD, ed intersects AB with E, FD intersects AC with F, the verification is: be = AF, AE = CF

Connect ad, ad = BD,
Angle B = angle fad,
Angle FDA = 90 degrees - angle ade = = angle EDB,
Triangle EBD and fad are congruent,
BE=AF,
AE=CF

As shown in the figure, in the triangle ABC, BD and CD bisect the angle ABC and the angle ACB respectively. ED is parallel to AB and FD is parallel to ac. if BC is equal to 6, find the perimeter of the triangle def

Ed parallel AB, FD parallel AC
Angle abd = angle BDE, angle ACD = angle CDF
BD and CD bisect angle ABC and angle ACB respectively
Angle DBE = angle BDE, angle DCF = angle CDF
The triangle BDE and DFC are isosceles
be=de,fd=fc
Cdef=6

In RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, if the circle with C as the center and R as the radius has only one common point with the hypotenuse AB, then the value range of R is___ ．

According to Pythagorean theorem, ab = 10 can be divided into two cases: ① as shown in Figure 1, when ⊙ C is tangent to AB, there is only one common point, then CD ⊥ ab. according to the area formula of triangle, s △ ABC = 12 × AC × BC = 12 × ab × CD, ⊥ 6 × 8 = 10 × CD, CD = 4.8, that is, r = 4.8. ② as shown in Figure 2, when the range of R is 6 < R ≤ 8, ⊥ C and ab have only one common point, so the answer is: r = 4.8 or 6 < R ≤ 8

In RT △ ABC, ∠ C = 90 °, AC = 5, BC = 12, if the circle with C as the center and R as the radius has a common point with the hypotenuse AB, the value range of R is obtained

Make CD ⊥ AB in D, as shown in the figure, ∵ ∠ C = 90 °, AC = 5, BC = 12, ∵ AB = ac2 + BC2 = 13, ∵ 12CD · AB = 12bc · AC, ∵ CD = 6013, ∵ when the circle with C as the center and R as the radius has a common point with the hypotenuse AB, the value range of R is 6013 ≤ R ≤ 12

In RT triangle ABC, AC = 3, BC = 4, if point C is the center of the circle and R is the radius of the circle with only one common point with hypotenuse AB, then the value range of R is?

Solution ∵ BC > AC,
The circle with C as center and R as radius has only one common point with hypotenuse ab
According to Pythagorean theorem, ab = 5
There are two cases
(1) When the circle is tangent to AB, r = CD = 3 × 4 △ 5 = 2.4;
(2) When point a is inside the circle and point B is on or outside the circle, AC ＜ R ≤ BC, i.e. 3 ＜ R ≤ 4
3 ＜ R ≤ 4 or r = 2.4

RT triangle ABC is a piece of iron plate, the remnant angle B = 6cm, ab = 8cm. Cut a square from it, so that point E is on side AB, point D is on side BC, and point FG is on side AC
Calculate the side length of the square, hoping to give the answer before 7:20

Angle B = 6cm?

In the triangle ABC, the angle B = 90 degrees, ab = 6cm, BC = 8cm, point P moves from point a along AB to B at 1 m / s, and point Q moves from B to BC at 2 m / s
For example, PQ starts from a and B at the same time. After a few seconds, the area of triangle PBQ is equal to 8 square centimeters?
For example, PQ starts from a and B at the same time, and after P reaches B, it continues to advance on the BC side, and after Q reaches C, it continues to advance on the CA side. After a few seconds, point q is on the AC side, so that the area of triangle PCQ is equal to 12.6 square centimeters?

(1) Let the area of the triangle PBQ be equal to 8 square centimeters after x seconds, then Pb · BQ = (ab-ap) BQ = (6-x) · 2x = 2.8 = 16, and the solution is x = 2 or x = 4
(2) Similarly, let the area of triangle PCQ be equal to 12.6 square centimeters after x seconds. According to the meaning of the title, AC = 10, q is on AC, so x > 4, and X

In RT △ ABC, what is the position relationship between the circle with C as the center and R as the radius and ab? Why? （1）r=2；（2）r=2.4；（3）r=3．

Let CD ⊥ AB be D. in the right triangle ABC, according to the Pythagorean theorem, if AB = 5, then CD = AC · bcab = 2.4; (1) when r = 2, 2.4 ＞ 2, the line and circle are separated; (2) when r = 2.4, the line and circle are tangent; (3) when r = 3, 2.4 ＜ 3, the line and circle intersect

It is known that in △ ABC, points D, e and F are points on BC, AB and AC respectively, AF is parallel to ED, and AF = ed, extend FD to point G, so that DG = FD, and verify that ED and Ag are equally divided,