1. As shown in the figure, AD=AC, BD=BC, O is a point above AB, so for congruent triangles, * * * in the figure is right.

2. As shown in the figure, △ ABC △ ade, then AB=, ∠E =∞. If BAE =120 and BAD = 40, then BAC =.

3. put two steel bars AA? 、BB？ The midpoint of the workpiece can be connected together to make a tool (caliper) to measure the groove width on the workpiece, as shown in the figure. If AB = 5 cm, the groove width is meters.

4. As shown in the figure, ∠A=∠D, AB=CD, then △△, based on.

5. As shown, in △ABC and △ABD, ∠C=∠D=90. If △ ABC△ Abd is proved by "AAS", a condition or; If you use "HL" to prove △ ABC △ Abd, you need to add conditions, or.

6. △ABC △ def, and the circumference of △ ABC is 12. If AB=3 and EF=4, then AC =.

7. When the master worker builds the door, as shown in the figure, the rectangular wooden frame ABCD is generally fixed with wooden strips EF to prevent deformation. It is for this purpose that the diamond-shaped movable iron gate is made of quadrangles.

8. As shown in Figure 5, in Δ AOC and Δ BOC, if AO=OB, ∠ 1=∠2, plus conditions, there is Δ δAOC?δBOC.

9. As shown in Figure 6, AE=BF, AD‖BC and AD=BC, then there are δ ADF ≌ and DF=.

10. As shown in Figure 7, in Δ ABC and Δ Def, if AB=DE and BE=CF, just add ∞ = ∠ or ‖ to prove Δ ABC Δ Def.

Second, multiple choice questions

1 1. as shown in the figure, BE=CF, AB=DE. Which of the following conditions can be added to derive △ ABC △ DFE ()?

(A)BC = EF(B)≈A =≈D(C)AC‖DF(D)AC = DF

12. It is known, as shown in the figure, AC=BC, AD=BD, and the following conclusion is incorrect ().

(a)co = do(b)ao = bo(c)ab⊥bd(d)△ACO?△bco

13. Take a point P in △ABC so that the distances between the three sides of the point P and △ABC are equal, then which three lines of △ABC should the point P intersect? ()

(a) The median line (d) of the bisector (c) with a high angle (b) is known as the median vertical line.

14. The following conclusion is correct ()

(a) Two right-angled triangles with equal acute angles are congruent; (b) A hypotenuse corresponds to the congruence of two equal right triangles;

(c) The congruence of two isosceles triangles with equal vertices and bases; Two equilateral triangles are congruent.

15. The following conditions can determine that a set of △ ABC △ def is ().

(A)A =∠D，∠C=∠F，AC=DF (B)AB=DE，BC=EF，∠A=∠D

(C)∠A=∠D, ∠B=∠E, ∠C=∠F (D)AB=DE, and the perimeter of △ABC is equal to that of △DEF.

16. As shown in the figure, in △ABC, AB=AC, AD is the angular bisector, and BE=CF, how many of the following statements are correct ()?

(1)AD bisection ∠ EDF; (2)△EBD?△FCD； (3)BD = CD； (4)AD⊥BC.

1 (B)2 (C)3 (D)4。

Third, answer questions:

1. As shown in the figure, AB=DF, AC=DE, BE=FC. Q: Are Δ Δ ABC and Δ Δ def identical? Are AB and DF parallel? Please explain your reasons.

2. As shown in the figure, is it known that AB=AC, AD=AE, BE and CD intersect at the congruence of O, δδABE and δδACD? State your reasons.

3. As shown in the figure, AC and BD intersect at O and are equally divided by O. Can AB‖CD be obtained, and AB=CD? Please provide a justification for the answer.

As shown in the figure, point A and point B are two points on both sides of the lake. In order to measure the distance between point A and point B, please design a scheme to measure the distance between point A and point B, and explain the feasibility of your scheme.

Verb (abbreviation of verb) reading comprehension questions

19.8 class (1) went to other places to have a math activity class. In order to measure the distance between a and b at both ends of the pond, the following scheme is designed:

(1) As shown in Figure 1, firstly, take a point C on the flat ground that can directly reach A and B, connect AC and BC, respectively extend AC to D and BC to E, so that DC=AC and EC=BC, and finally measure the distance of DE as the length of AB;

(Figure 1)

(2) As shown in Figure 2, first pass through point B as the perpendicular BF of AB, then take two points C and D on BF to make BC=CD, then pass through point D as the perpendicular DE of BD, and pass through the extension line of AC at point E, then the length of DE is the distance of AB.

(Figure 2)

Answer the following questions after reading:

(1) Is Scheme (Ⅰ) feasible? Please provide a justification for the answer.

(2) Is Scheme (Ⅱ) feasible? Please provide a justification for the answer.

(3) The purpose of BF ⊥ AB and ED⊥BF in scheme (II) is: If only ∠ Abd = ∠ BDE ≠ 90 is satisfied, is Scheme (Ⅱ) established? .

Reference answer:

First, fill in the blanks:

1.3; 2.AD，∠C，80； 3.5 cm; 4. A Bo, DCO, AAS5.∠CAB=∠DAB, ∠CBA=∠DBA, AC=AD, BC = BD6.5; 7. Stability and instability of triangles; 8.CO = CO9.△BCE，CE； 10.b，DEF，AB，DE

Second, multiple-choice questions:11-16: dabcad

Iii. Answer the question: 1. Yes; 2. Yes, the reason is slight; 3. Triangle congruence; leave out

Fourth, reading comprehension questions:

(1) Yes; (2) Yes; (3) Constructing triangular congruence energy