Math and geometry proof questions and answers in the second day of junior high school

. When Rt△ABC, ∠ BAC = 90, take a point D on BC so that BD=AB, E is the midpoint of BC, and ef ∠ AD, AB cross to F. Verification: DF=BC/2.

2。 It is known that AD is the height on the hypotenuse BC of Rt△ABC, the bisector of ∠B in M intersects with AD, that of AC in E, and that of ∠DAC in N intersects with CD ... It is proved that the quadrilateral is a diamond.

3。 In trapezoidal ABCD, the bisector of AD‖BC and ∠ABC intersects CD at E, and E is the midpoint of DC. Verification: CD=AD+BC

4。 At Rt△ABC, ∠ BAC = 90, AD⊥BC, the vertical foot is D, and it is divided equally ∠ABC passes through AD to E, and EF ∠ BC passes through AC to F. Verification: AE = CF.

5.△PCD, take any point E on the PC and connect it with ED; Take any point f on PD and connect CF; Connect AB through point E.F as BE‖CF and AF‖DE respectively. Verification: AB‖CD

6. An equilateral triangle is known, and the distance from one point inside to each vertex is 3.45. What is the side length of a triangle?

Seven .. (The full mark of this question is 6) As shown in the figure, DB‖AC, and DB = AC, and E is the midpoint of AC. Verification: BC = DE.

8. As shown in the figure, in the square ABCD, points E and F are on CD and BC respectively, BF = Ce, and the connecting lines BE and AF intersect at point G, then the following conclusion is correct ().

(A)BE = AF(B)∞DAF =∞BEC

(c)AFB+∠bec = 90(d)ag⊥be

9. (Huanggang, Hubei, 2002) It is known that as shown in figure 1, cd⊥bd ab⊥bd, the vertical foot is B, D, AD and BC intersect at point ef⊥bd e, and the vertical foot is F, which can be proved (no need for candidates to prove).

If the vertical line in figure 1 is changed to oblique, as shown in figure 2, AB‖CD, AD and BC intersect at point E,

If point E is EF‖AB and BD is paid at point F, then:

(1) Is it still valid? If yes, please give proof; If not, please explain the reasons;

(2) Please find out the relationship between S△ABD, S△BED and S△BDC and give proof.

1. As shown in the figure, take the AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE to connect EG outward.

Verification:

2. As shown in the figure, take the AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect EG, if O is the midpoint of EG.

Verification: EG=2AO

3. As shown in the figure, take the AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect EG. If O is the midpoint of EG, the extension line of OA intersects BC at H point.

Verification: AH⊥BC

4. As shown in the figure, take the AB side and AC side of △ABC as sides respectively, and connect EG with square ABFG and ACDE outward. If AH⊥BC, the extension line of HA intersects EG at O point.

Prove that O is the midpoint of EG.

5. As shown in the figure, take AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect BE and CG.

Verification:

( 1)BE=CG

(2)BE⊥CG

6. As shown in the figure, take AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect BE and CG.

Let FM⊥BC, DN⊥BC be the extension line of the intersection CB of point M and the extension line of the intersection BC of point N.

Verification: FM+DN=BC

7. As shown in the figure, take AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect BE, CG and FD.

O is the midpoint of FD, and OP⊥BC is at point P.

Verification: BC=2OP

8. As shown in the figure, take AB side and AC side of △ABC as sides respectively, and make square ABFG and ACDE outward to connect CE, BG and GE.

M, n, p and q are the midpoint of EG, GB, BC and CE respectively.

Prove that quadrilateral MNPQ is a square

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