Mathematics, nine on, proof, calculations about trapezoids

Passing the point D is made of DG, and the vertical BC is crossed with G. Then the triangle BEF is similar to the triangle chain ascending GDC and gc=4-1=3=dg=ab=2eb. So EB = 3/2. Then from the Pythagorean shed scattered old slag digging theory, EF = 3/2 of the number 2

Pythagorean theorem.

1.If the leak is ab on the side, the height will always be bc

Then the triangle area is 10x10 2=10

2.Take BC as one side. Then be=15, bc=10, using the Pythagorean theorem to obtain ce=root number 125Only socks, i.e., 5 roots, 5 three-finger liquids, with an area of 10x5, 5 roots, 5 2 = 25, 5 roots, 5 <>

Because ABC is an isosceles ladder sedan deformed, angle b = angle trembling c, as df ab, then the closed angle c = angle dfc, ab = df = cd = 6, ad = bf = 5, cf = bc-bf = bc-ad = 3

So the circumference of the triangle is 6+6+3=15

As AE DC, the angle c=70°, so the angle AEB=70°

In AEB, the angle b=55°, so the angle EAB=55°, equiangular to the equiside, AE=BE=5

So dc=ae=5

In the isosceles coarse reed trapezoidal ABCD, bending delay a= d, c = bad bc

Rock belt c + d = 180

then c+ a=180

Because AD is parallel to BC angle ACB = angle DAC

And the angle b = the angle AED, so the triangle ABC is similar to the ADE.

And because of the pretense ab=3 bc=4, so ac=5

By the source of the lack of Chang in the similar AD than AC and hail de than AB equal. de=

∠b=90º

ac= (ab +bc )=3 +4 wreckage) = 5 abc area = ab bc 2=3 4 2=6 trapezoidal area = (ad+bc) ab 2=(2+4) 3 2=9 adc area = trapezoidal area - abc area = 9-6=3de acde ac 2=3

i.e.: de 5 2 = 3

de=6/5

ac*de=ad*ab means that the area of the triangle with the same base is equal.

The area of the ADC can be based on AC, and DE can be the height on the edge of AC; You can also use AD as the bottom, and AB is the height on the side of AD.

1 2ac*de=1 2ad*ab are all areas of a triangular acd, so ac*de=ad*ab

<> do and bury de bc to hand over bc to e

de=ab=ad=be=1

ec = cd -de = 3 -1 = 2 2 trapezoidal ABCD full area.

1+1+2 2 *1 2=1+ first 2