1. If the complementary angle of an angle is 150, then the complementary angle of this angle is ().
A.30 B.60 C.90 D. 120
2. The correct proposition in the following propositions is ()
A. the acute angle is greater than its complementary angle B. The acute angle is greater than its complementary angle.
C. the obtuse angle is greater than its complementary angle d, and the sum of acute angle and obtuse angle is equal to a right angle.
3. As shown in the figure ∠ ACB = 90, CD⊥AB, and the vertical foot is D. The following conclusion is wrong ().
A. there are three right triangles.
B.∠ 1=∠2
C.∠ 1 and ∠B are complementary angles of ∠ a.
D.∠2=∠A
(Question 3)
4. The complementary angle of acute angle is greater than its complementary angle _ _ _ _ _.
5.∠ 1, ∠2 are complementary angles, and ∠1> ∠ 2, then the complementary angle of∠ 2 is ()
A.(∠ 1+∠2)b .∠ 1 c .(∠ 1-∠2)d .∠2
6. The complementary angle of an angle is 42, which is more than twice its complementary angle. Find the degree of this angle.
Second, the vertex angle
7. The following statement is true ()
A. If two angles are diagonal, they are equal; If two angles are equal, they are antipodal angles.
C. If two angles are not equal, they are not antipodal angles; D. None of the above judgments are correct.
8. Write the proposition "the vertex angles are equal" in the form of "if ..."
9. As shown in the figure, the vertex angle * * * has ().
A.6 right
B. 1 1 Right
C. 12 pair
D. 13 pair
(Question 9)
10. In the figure below, ∠ 1 and ∠2 are opposite to the vertex angle, but ().
1 1. As shown in the figure, it is known that straight lines A and B intersect, ∠ 1=∠2, ∠3, ∠4.
12. As shown in the figure, ∠α+∞β= 80 is known. Find the degrees of ∠ α and ∠γ.
Third, parallel lines
13. The following statement is true ()
One and only one straight line is parallel to the known straight line;
B. straight line AB∑CD, then straight line AB must also be parallel to ef;
C a straight line is perpendicular to one of the two parallel lines and must also be perpendicular to the other;
D. Two lines that never intersect are called parallel lines.
14. If a∨b and b∨c, then a∨c is based on ().
A. Equivalent substitution B. Parallel axiom
C. Two lines parallel to the same line are parallel; D. The isosceles angles are equal and the two straight lines are parallel.
15. If two parallel lines are cut by a third straight line, the bisectors of a pair of intersecting angles are each other ().
A. parallel B. bisecting C. intersecting but not perpendicular D. perpendicular
16. as shown in the figure, DH∨EG∨BC, DC∨ef. Then the number of angles equal to ∠BFE (excluding ∠BFE) is ().
A.2 B.3 C.4 D.5
17. If two parallel straight lines are cut by a third straight line, () can be formed.
A.4 pairs of vertex angles and 4 pairs of congruent angles.
B. Two pairs of internal parts are staggered and two pairs of congruent angles.
C. two pairs of isosceles angles and two pairs of internal angles on the same side.
D. Two pairs of internal angles and four pairs of internal angles on the same side.
18. As shown in figure 1, from ∠ 1=∠2, it can be determined that AB∨CD is based on _ _ _ _ _ _ _ _, as shown in figure 2, from ∠ 1 =∞. As shown in figure 3, ∫≈ 1 =∠2 (known), ∴ de ∥ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
( 1) (2) (3)
19. As shown in the figure, ∫≈ 1 = 130, ∠ 2 = 50 (known).
∴∠ 1+∠ 2 = 180 (the nature of the equation)
∴AB∥CD(_______).
(Question 19) (Question 20) (Question 2 1)
20. As shown in the figure, l 1∨L2∨L3 is known.
(1) If ∠ 1 = 70, ∠ 2 = _ _ _ _ _ _ _ _ _ _ _;
② If ∠ 1 = 70, ∠ 3 = _ _ _ _ _ _ _ _ _;
③ If ∠ 1 = 70, ∠ 4 = _ _ _ _ _ _ _.
2 1. As shown in the figure, the straight line DE passes through point A, DE∥BC, ∠ B = 44, ∠ C = 57.
So:
( 1)∠DAB = _ _ _ _ _ _ _()；
②∠EAC = _ _ _ _ _ _ _()；
(3)∠BAC = _ _ _ _ _ _ _()；
(4)∠BAC+∠B+∠C=______()。
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Innovative application
22. Proposition A: The isosceles angles are equal and the two straight lines are parallel.
Proposition B: Two straight lines are parallel and have the same angle.
The following statement is true ()
A. Propositions A and B are parallel lines. B. propositions a and b are not parallel lines.
C. only proposition a is a parallel line. D. only proposition b is a parallel line.
23. As shown in the figure, if AB∨CD, then ①∠ 1=∠2, ②∠3=∠4,
③ ∠ 1+∠ 3 = ∠ 2+∠ 4. The correct conclusion is ()
A. only1b. Only 2c. Only 3d ① ② and ③.
Mathematics in life
24. As the picture shows, it is a solid wall with two sides. In order to get its angle, we can neither enter the wall nor tear it down. Q: How can I get its degree?
Trace the origin of things
25. As shown in the figure, ∠ 1=∠2, EC∨AC, verification: ∠ 3 = ∠ 4.
Proof: ∫EC∨AD
∴∠ 1=_______(______)
∠2=_______(________)
∵∠ 1 =∠ 2 (_ _ _ _ _)
∴∠3=∠4(________).
26. As shown in the figure, ∠ 1+∠ 3 = 180, ∠ 2+∠ 3 = 180.
Verification: AB∑CD
Proof: ∫∠1+∠ 3 =180 (_ _ _ _ _ _)
∴∠ 1 and ∠3 are complementary (_ _ _ _ _ _)
∵∠2+∠3= 180 (________)
∴∠2 and∠∠∠ 3 are complementary (_ _ _ _ _ _)
∴∠ 1=_______(________)
∴AB∥CD(________).
27. Known: as shown in the figure, ∠FMN=∠C, ∠FNM=∠B, and verified: ∠ A = ∠ F.
Inquiry learning
There are 2 005 straight lines a 1, a2, …, a2005 on the same plane. If a 1⊥a2, a2∨a3⊥a4, a4∨a5, …, what is the positional relationship between a 1 and a2005?
Answer:
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1.b Analysis: This angle is 30.
2.c analysis: Counterexample: the complementary angle of 30 is 60, so A is wrong, and the complementary angle of 30 is 150.
So b is wrong, 30+ 120 = 150 is not a right angle, so d is wrong.
3.B
4.90 Analysis: Let the degree of this angle be x,
180-x-(90-x)= 180-x-90+x = 90
5.C
6. let the degree of this angle be x, according to the meaning of the question:
180 -x-42 =2(90 -x)
138 -x= 180 -2x
x=42
So, the degree of this angle is 42.
7.A
8. If two angles are diagonal, then the two angles are equal.
9.A 10。 D
1 1.∵∠ 1+∠2= 180 ,∠ 1=2∠2
∴2∠2+∠2= 180
∴∠2=60 ,∠ 1= 120
∠ 1 and∠ 3, ∠2 and ∠4 are antipodal angles.
∴∠ 1= 120 ,∠2=60 ,∠3= 120 ,∠4=60 .
12.∠∠α and ∠∠ β are antipodal angles, ∠∠∠ α+∠ β = 80.
∴∠α=∠β=40
∵∠ α+∠ γ = 180.
∴∠γ= 180 -∠α= 180 -40 = 140
∴∠α=40 ,∠γ= 140 .
13.C 14。 C 15。 A 16。 D 17。 A
18. The congruence angle is equal, the internal angle of two parallel lines is equal, and the two parallel lines are parallel to BC.
The isosceles angles are equal and the two straight lines are parallel.
19. The internal angles on the same side are complementary and the two straight lines are parallel.
20.① 1 10 Two straight lines are parallel and complementary.
② 70 Two straight lines are parallel and have the same angle.
③ 70 Two straight lines are parallel and the internal dislocation angles are equal.
2 1.( 1) 44 Two straight lines are parallel, and the internal dislocation angles are equal.
(2) At 57, two straight lines are parallel, and the internal dislocation angles are equal.
(3) The sum of the internal angles of 79 triangles is equal to 180.
(4) The sum of the internal angles of the triangle 180 is equal to180.
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22.d analysis: Proposition A is a judgment theorem of parallel lines.
23.D
24. Extend outward from the corner to get the diagonal of the corner.
25.∠ 3 Two straight lines are parallel and the same angle is equal ∠4 Two straight lines are parallel and the internal dislocation angle is equal.
Known equivalent substitution
26. The definition of known complementary angle is known ∠2. Equivalent substitution internal angles are equal and two lines are parallel.
27.∫∠fmn =∠c (known),
∴DF∥AC (internal dislocation angles are equal and two straight lines are parallel)
∴∠A=∠FDB (two straight lines are parallel with the same angle)
Also ≈FNM =∠B (known)
∠NMF=∠DMB (equal vertex angles)
∴∠BDM=∠MFN (the sum of the inner angles of the triangle is equal to 180).
∴∠A=∠F (equivalent substitution).