.
2. As shown in figure 1, it is known that △ OCA △ OBD, C and B, D and A are the corresponding vertices, and the equilateral of these two triangles is.
3. As shown in Figure 2, it is known that △ ABC △ ade, ∠B and ∠D are corresponding angles, so AC sum is corresponding edges.
∠BAC and are corresponding angles.
Figure 3 Figure 4
4. The angular bisectors AM and BN of 4.△ ABC intersect at point I, so the distance from point I to the edge is equal, and CI must be equal.
5. As shown in Figure 3, it is known that D is on the BC side, DE⊥AB is on the E side, DF⊥AC is on the F side, DE=DF, B = 50, C = 70,
Then ∠DAF=, ∠ ade =.
6. As shown in Figure 4, if AB=BE, BC=BD, ∠ 1=∠2, then AC=, ∠ABC=.
A
Figure 5 Figure 6
7. To a point with equal distance on both sides of a corner, at.
8. As shown in Figure 5, it is known that △ ABC △ def, corresponding side AB=DE, corresponding angle ∠B=∠DEF,.
9. As shown in Figure 6, △ ABC △ dec is known, where AB=DE, ∠ ECB=30, then ∠ACD=.
10. As shown in Figure 7, it is known that AB = AD, ∠ 1 = ∠ 2, to make △ ABC △ ade,
The conditions that need to be added are. (Fill in only one)
Second, multiple-choice questions (3 points for each question, *** 18 points)
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 to make the distance between the three sides of the point P and △ABC equal, then which three lines of △ABC should the point P intersect ()?
(a) High (b) Angle bisector (c) Middle line (d) perpendicular bisector
14. The following conclusion is correct ()
(a) Two right triangles coincide with two equal acute angles; (b) Two right triangles coincide with a hypotenuse;
(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
Three. Answer: (7 points for each question, ***42 points)
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.
4. As shown in the right figure, AB = AD, ∠ AB=AD = ∠ CAE, AC=AE, and verification: CB=ED.
5. Known: As shown in the figure, AB = CD, AB ‖ DC.
Verification: AD‖BC, ad = BC
6. It is known that, as shown in the figure, AO divides ∠EAD and ∠EOD equally. Verification: ①△AOE?△AOD2EB = DC.
Verb (abbreviation of verb) reading comprehension question (10 mark)
Students from Class 8 (1) go to other places to have math activity classes. 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;
(2) As shown in Figure 2, first pass through point B as the vertical line BF of AB, then take two points C and D on BF to make BC=CD, then pass through point D as the vertical line of BD and pass through the extension line of AC at point E, and then measure the length of DE as the distance of AB.
Figure 1 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: As long as you are satisfied
∠ Abd =∠ BDE = 90. Is Scheme (2) effective?