I. Fill in the blanks (30 points)
(1) If 0 < α < 90, the complementary angle of 90-α is a, and the angle is 90 +a A.
(2) As shown in the following figure (1), ∠ 1=∠5, then ∠3 = ∠7, ∠4 = ∠6, ∠ 1+∞.
(3) As shown in the following figure (2), ∠ 2 = ∠ 3, ∠ 1 = 62 24', then ∠ 4 = 62.4.
(4) As shown in the following figure (3), if ∠ 1 is equal to the remaining angles, and ∠2 is equal to three times the remaining angles, then l 1 and the position of l2.
The relationship is parallel.
(5) As shown in Figure (4), FA is the bisector of ∠CFE. If ∠ 1 = 40, ∠ 2 = 70 ∠ EFB = 1 10.
( 1) (2) (3) (4)
(6) The proposition that the complementary angles of the same angle are equal is a true proposition, and it is written in the form of "If …… then ………"
If two angles are complementary angles of the same angle
Then they are equal.
(7) If the line segment PO and the line segment AB are perpendicular to each other, and the point O is between A and B, let the distance from P to AB be m,
If the distance from P to A is n, then the relationship between M and N is that m(8)C is the midpoint of line AB, D is a point on line CA, and E is.
The midpoint of the AD line, if BD=6, EC= 3.
(9) As shown in the following figure, OA⊥OB,∠AOD= ∠COD, ∠BOC=3∠AOD,
Then the degree of ∠COD is 30.
Second, multiple-choice questions (18 points)
1. Among the following propositions, the pseudo-proposition is (d)
A. If you cross a point, you can make a straight line perpendicular to the known straight line.
If a straight line is perpendicular to one of the two parallel lines, it must be perpendicular to the other.
C two lines parallel to the same line are parallel.
D. Two lines perpendicular to the same line are vertical.
2. Of the two complementary angles, two times of one angle is smaller than three times of the other angle 10, and these two angles are (b).
A. 104，66 B. 106，74 C. 108，76 D. 1 10，70
3. As shown in the figure below, AB‖CD‖EF, and AF‖CG. The angle (not counting itself) equal to ∠A in the figure has (b).
A.5 B.4
C.3 D.2
4. Given a straight line l 1, l2 and l3 are on the same plane. If l 1⊥l2 and l2‖l3, the positional relationship between l 1 and l3 is (c).
A. Parallel B. Intersecting C. Vertical D. None of the above is correct.
5. If the two sides of ∠A and ∠B are parallel, then the relationship between ∠A and ∠B is (D).
A.b. Complementarity or complementarity
C. Complementarity D. Equality or complementarity
6. As shown in the figure below, point E is on the extension line of BC, and it cannot be judged that AB‖CD is (A) under the following conditions.
A.∠3=∠4 B.∠ 1=∠2
C.∠B =∠DCE D∠D+∠DAB = 180
Iii. Judgment (18)
The complementary angles of (1) vertex angles are equal. (right)
(2) The bisectors of adjacent complementary angles are perpendicular to each other. (right)
(3) Only one vertical line can be drawn on the plane. (error)
(4) Two straight lines that do not intersect in the same plane are called parallel lines. (right)
(5) If a straight line is perpendicular to one of the two parallel lines,
Then this straight line is perpendicular to another straight line among the parallel lines. (right)
(6) Two straight lines are cut by a third straight line, and the sum of two pairs of internal angles on the same side is equal to a fillet. (right)
(7) The distance from a point to a straight line is the length of the perpendicular from this point to this straight line. (error)
(8) Axiomatization: One and only one straight line is parallel to the known straight line and intersects a point outside the straight line. (right)
(9) The vertical section from a point outside a straight line to this straight line is called the distance from this point to this straight line. (error)
Four, answer questions (54 points)
1. As shown in the following figure, EO⊥AB is in O, and the straight line CD passes through O, ∠ EOD: ∠ EOB = 1: 3, and find the degrees of ∠AOC and ∠AOE.
Solution: let EOD angle be X.
3x = 90°
X=30
DOB = 90-30 = 60。
Because: angle DOB= angle AOC (equal to vertex angle)
So: angle AOC=60.
Because: AB is a straight line (known)
So: angle AOB = 180.
Because: angle AOE= angle AOB- angle EOB
So: AOE = 180-90.
=90
Answer: AOE=90, AOC=60.
2. Given that the difference between two complementary angles is equal to 40 30 ˊ, find the complementary angle of the smaller angle.
Solution: Let the larger angle be x 。
X-( 180-x)=40.5
x- 180+x=40.5
X+X =40.5+ 180
2X=220.5
X= 1 10.25
The smaller angle is:180-110.25 = 69.75.
The complementary angle of the smaller angle is: 90-69.75 = 20.25.
A: The complementary angle of the smaller angle is 20.25.
3. As shown in the figure, AB‖CD, ∠ 1=∠2, ∠3=∠4, find the degree of ∠FPE.
Solution:
AB | | CD (known)
∴ (∠ 3+∠ 4)+(∠1+∠ 2) =180 (two straight lines are parallel and the internal angles on the same side are complementary).
∠∠ 1 =∠2, ∠3=∠4 (known)
∴ 2 ∠ 3+2 ∠ 1 = 180 (equivalent substitution)
∴2(∠ 1+∠3)= 180