Work Sheet Of Angles
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LINES AND ANGLES I. POSITION OF TWO LINES AND TYPES OF ANGLES A. POSITION OF TWO LINES There are 3 kinds of position of lines: 1. Parallel 2. Intersecting 3. Crossing (not parallel and also not intersecting) B. TYPES OF ANGLES The component of an angle A
B C
The angle on the left is ∠ B or ∠ ABC The components of an angle are: Side BA and BC are called LEG Point B is called VERTEX Area of the angle
Types of Angles 1. Acute angle ( 00 – 900 ) 2. Right angle ( 900 ) 3. Obtuse angle ( 900 – 1800 ) 4. Straight angle ( 1800 )
WORK SHEET 1. Look at the cuboids below. H G a. Determine the position of two lines based on the cuboids. E F Fill by parallel, intersection, or crossing Line AB and EF are ������. D C Line AE and AD are ������... B A Line BC and DH are ������ b. Determine the couple of the line that is parallel. Line AD and �� Line FG and ��. Line GH and �� c. Determine the couple of the line that is intersecting. Line DC and �� Line EH and ��. Line CG and ��. d. Determine the couple of the line that is crossing. Line CD and ��. Line DH and ��. Line EF and ��
2. Look at the angles below. C
D
M
i
.
W
K
E
X
Q
R ii
P
L iii
T
Y iv
S
U v
a. For every angle determine the legs, the vertex, and the name of the angle ( using 3 letters) i. name of angle is ∠ CDE ; the legs are DC and … ; the vertex is …. ii. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. iii. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. iv. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. v. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. b. Measurement every angle and determine the type of each angle. i. ∠ CDE = … and the type is …………………………. ii. ∠ …… = … and the type is …………………………. iii. ∠ …… = … and the type is …………………………. iv. ∠ …… = … and the type is …………………………. v. ∠ …… = … and the type is …………………………. 3. Look at the cuboids below. A
D
B
O
C
a. Determine the couple of angle that have the sum of angle is 900. - ∠ ADO and ∠ CDO ; ∠ ADO + ∠ CDO = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900
Two angles having the total sum of 900 are called Complementary angles. One of the angles is the complement of the other angle.
b. Determine the couple of angle that have the sum of angle is 1800. - ∠ DOC and ∠ COB ; ∠ DOC + ∠ COB = 1800 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 - ∠ …….and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 - ∠ …….and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 Two angles having the total sum of 1800 are called Supplementary angles. One of the angles is the supplement of the other angle. C. TWO LINES INTERSECTED BY A TRANVERSAL LINE. m 1
2 4
k 3 5
6 8
l 7
Look at the figure above. Line k and line l are intersected with line m. The properties of that condition are: 1. Corresponding angles, i.e. ∠ 1 and ∠ 5. 2. Alternate interior angles, i.e. ∠ 3 and ∠ 5. 3. Alternate exterior angles, i.e. ∠ 1 and ∠ 7 4. Interior angles on the same side of the transversal, i.e. ∠ 4 and ∠ 5 5. Exterior angles on the same side of the transversal, i.e. ∠ 1 and ∠ 8 6. Vertical angles, i.e. ∠ 1 and ∠ 3
WORK
SHEET
1. Look at the figure below. c 1 2 6 5
4 3 7
a
b
8
Determine the couple of angles based on the properties on the figure above. a. The Corresponding angles - ∠ 1 and ∠ … - ∠ … and ∠ …. - ∠ … and ∠ …. - ∠ … and ∠ …. b. The Alternate interior angles - ∠ 3 and ∠ …. - ∠ … and ∠ …. c. The Alternate exterior angles - ∠ 1 and ∠ …. - ∠ … and ∠ …. d. Interior angles on the same side of the transversal - ∠ 2 and ∠ …. - ∠ … and ∠ …. e. Exterior angles on the same side of the transversal - ∠ 1 and ∠ ….
-
∠ … and ∠ …..
-
∠ ∠ ∠ ∠
f. Vertical angles
1 and ∠ …. … and ∠ …. … and ∠ …. … and ∠ ….
2. Look at the figure below.
1000 c d g
e f
b
a
Line p and line q are parallel and those are intersecting to line t. Determine the measure of a, b, c, d, e, f, and g. - a = 1800 - �= � (supplementary angles) - b = �� (vertical angles) - c = ��. (vertical angles with � - d = ��.. (form by the equal line and parallel line with 1000) � - e = �.. (supplementary angles) - f = ��.. (vertical angles) - g = ��.. (vertical angles)
B C
The angle on the left is ∠ B or ∠ ABC The components of an angle are: Side BA and BC are called LEG Point B is called VERTEX Area of the angle
Types of Angles 1. Acute angle ( 00 – 900 ) 2. Right angle ( 900 ) 3. Obtuse angle ( 900 – 1800 ) 4. Straight angle ( 1800 )
WORK SHEET 1. Look at the cuboids below. H G a. Determine the position of two lines based on the cuboids. E F Fill by parallel, intersection, or crossing Line AB and EF are ������. D C Line AE and AD are ������... B A Line BC and DH are ������ b. Determine the couple of the line that is parallel. Line AD and �� Line FG and ��. Line GH and �� c. Determine the couple of the line that is intersecting. Line DC and �� Line EH and ��. Line CG and ��. d. Determine the couple of the line that is crossing. Line CD and ��. Line DH and ��. Line EF and ��
2. Look at the angles below. C
D
M
i
.
W
K
E
X
Q
R ii
P
L iii
T
Y iv
S
U v
a. For every angle determine the legs, the vertex, and the name of the angle ( using 3 letters) i. name of angle is ∠ CDE ; the legs are DC and … ; the vertex is …. ii. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. iii. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. iv. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. v. name of angle is ∠ … … …; the legs are … and … ; the vertex is …. b. Measurement every angle and determine the type of each angle. i. ∠ CDE = … and the type is …………………………. ii. ∠ …… = … and the type is …………………………. iii. ∠ …… = … and the type is …………………………. iv. ∠ …… = … and the type is …………………………. v. ∠ …… = … and the type is …………………………. 3. Look at the cuboids below. A
D
B
O
C
a. Determine the couple of angle that have the sum of angle is 900. - ∠ ADO and ∠ CDO ; ∠ ADO + ∠ CDO = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 900
Two angles having the total sum of 900 are called Complementary angles. One of the angles is the complement of the other angle.
b. Determine the couple of angle that have the sum of angle is 1800. - ∠ DOC and ∠ COB ; ∠ DOC + ∠ COB = 1800 - ∠ …… and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 - ∠ …….and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 - ∠ …….and ∠ ……. ; ∠ ……. + ∠ ……. = 1800 Two angles having the total sum of 1800 are called Supplementary angles. One of the angles is the supplement of the other angle. C. TWO LINES INTERSECTED BY A TRANVERSAL LINE. m 1
2 4
k 3 5
6 8
l 7
Look at the figure above. Line k and line l are intersected with line m. The properties of that condition are: 1. Corresponding angles, i.e. ∠ 1 and ∠ 5. 2. Alternate interior angles, i.e. ∠ 3 and ∠ 5. 3. Alternate exterior angles, i.e. ∠ 1 and ∠ 7 4. Interior angles on the same side of the transversal, i.e. ∠ 4 and ∠ 5 5. Exterior angles on the same side of the transversal, i.e. ∠ 1 and ∠ 8 6. Vertical angles, i.e. ∠ 1 and ∠ 3
WORK
SHEET
1. Look at the figure below. c 1 2 6 5
4 3 7
a
b
8
Determine the couple of angles based on the properties on the figure above. a. The Corresponding angles - ∠ 1 and ∠ … - ∠ … and ∠ …. - ∠ … and ∠ …. - ∠ … and ∠ …. b. The Alternate interior angles - ∠ 3 and ∠ …. - ∠ … and ∠ …. c. The Alternate exterior angles - ∠ 1 and ∠ …. - ∠ … and ∠ …. d. Interior angles on the same side of the transversal - ∠ 2 and ∠ …. - ∠ … and ∠ …. e. Exterior angles on the same side of the transversal - ∠ 1 and ∠ ….
-
∠ … and ∠ …..
-
∠ ∠ ∠ ∠
f. Vertical angles
1 and ∠ …. … and ∠ …. … and ∠ …. … and ∠ ….
2. Look at the figure below.
1000 c d g
e f
b
a
Line p and line q are parallel and those are intersecting to line t. Determine the measure of a, b, c, d, e, f, and g. - a = 1800 - �= � (supplementary angles) - b = �� (vertical angles) - c = ��. (vertical angles with � - d = ��.. (form by the equal line and parallel line with 1000) � - e = �.. (supplementary angles) - f = ��.. (vertical angles) - g = ��.. (vertical angles)
