(08 Chenzhou, Hunan, 27 questions) (the full score of this question is 10) as shown in figure 10. In the parallelogram ABCD, AB = 5, BC = 10, the height of BC side is AM=4, and E is.

The moving point on the side of BC (not coincident with B and C). The vertical line passing through e is straight line AB, and the vertical foot is F.

The extension lines of FE and DC intersect at G point, connecting DE and DF. ....

( 1)

Verification: BEF

√δCEG。

(2)

What is the relationship between the perimeter of △BEF and △CEG when point E moves on BC line? And explain your reasons.

(3) let be = x, and the area of △DEF is

Please find out the functional relationship between y and x, what is the value of x, and what is the maximum value of y?

(Analysis of 27 Questions in Chenzhou, Hunan Province in 2008) (1)

Because the quadrilateral ABCD is a parallelogram,

therefore

1 point

therefore

therefore

3 points

(2)

The sum of the perimeters of is a constant value.

4 points

Reason 1: When FG crosses the parallel line of point C and intersects the straight line AB in H ..

Because GF⊥AB, quadrilateral FHCG is a rectangle. therefore

FH=CG，FG=CH

Therefore,

The sum of the perimeters of is equal to BC+CH+BH.

pass by

Bc = 10, AB = 5, AM = 4, CH = 8, BH = 6,

So BC+CH+BH = 24.

. . . 6 points

Reason 2: As can be seen from AB = 5 and AM = 4,

In Rt△BEF and Rt△GCE, there are:

So the circumference of △BEF is

△△ ECG circumference is

And be+ce = 10, so

The sum of perimeters is 24.

6 points

(3) let be = x, then

therefore

8 points

Formula:

.

So, when?

When y has the maximum value.

9 points

The maximum value is

.

10 point

Example 3. (08 Wenzhou, Zhejiang) As shown in the figure, in

Yes,

They are the edges.

The midpoint of.

From the point of view,

Leave the edge

Direction movement, crossing point

work

what

, a little.

work

transmit

what

, when the key.

Yudian

When overlapping, the points

Do n't move a set of

.

(1) Find the point

reach

distance

Length;

(2) seeking

About; In all parts of; about

Function relation of (no need to write the range of independent variables);

(3) Is it meaningful?

, make

Isosceles triangle? If it exists, request all those that meet the requirements.

The value of; If it does not exist, please explain why.

6.

Solution: (1)

.

main points

for

Midpoint,

.

.

.

(2)

.

, namely

About; In all parts of; about

The functional relationship of is:

.

(3) Existence can be divided into three situations:

① When?

When, a little.

work

what

, then

.

.

.

② When?

When,

.

③ When?

So, when?

for

A point on the vertical, so it is a point.

for

The midpoint of,

.

All in all, when

for

Or 6 or

When,

It is an isosceles triangle.

46. (Qingdao, Shandong, 2009) As shown in the figure, in the trapezoidal ABCD,

, point

Starting from B, move at a constant speed along the BD direction at the speed of 1 cm/s; At the same time, the line segment EF starts from DC and moves in the direction of DA at a constant speed of1cm/s.

At q, connect PE. If the exercise time is

(s)(

). Answer the following questions:

(1) When

Why are you on duty?

?

(2) Settings

The area of is

(cm2), find

and

The functional relationship between them;

(3) Is there a moment?

, make

? If it exists, find out this time.

The value of; If it does not exist, explain why.

(4) Connection

In the above movement, the Pentagon

Has the area changed? Explain why.

Congruent triangles's nature and judgment, similar triangles's judgment and calculation.

Answer: (1)√.

∴

. and

,∴

,∴

.

Suffer from hell

.

(2)∵

Parallel and equal

Quadrilateral

It is a parallelogram.

.

∵

,∴

. ∴

. ∴

.

. ∴

.

Guo b Zuo

, pay

what

, too

work

, pay

what

.

.

∵

,∴

. and

.

(3)

. if

, yes

solve

.

(4) in

and

Yes,

∴

.

∴ In the process of movement, pentagons

The area of the remains unchanged.