Download Geometry G2 HW 2 Special Angles and Angle

Geometry G2 HW 2
Due 9/13
Special Angles and Angle Relationships
Standard MTH.PPF.251 Exhibit some knowledge of the angles associated with parallel lines
1. Using the picture above, name 4 sets of vertical angles.
2. Using the picture above, name 4 sets of corresponding angles
3. Using the picture above, name 4 sets of alternate interior angles
4. Using the picture above, name 4 sets of linear pairs
5. Using the picture above, name 4 sets of alternate exterior angles
Standard MTH.PPF.351 Find the measure of an angle using properties of parallel lines
6. In the figure below, parallel lines l and m are intersected by the transversal t. Based on the information given in the
figure, find x.
x°
l
139°
m
t
7. In the figure below, parallel lines l and m are intersected by the transversal t. Based on the information given in the
figure, find x.
l
x°
141°
m
t
8. In the figure below, parallel lines l and m are intersected by the transversal t. Based on the information given in the
figure, find x.
l
144°
m
x°
t
9. Find
The diagram is not to scale.
Q
R
76°
42°
Standard MTH.PPF.352 Exhibit knowledge of basic angle properties and special sums of angle measures
10. Name an angle supplementary to
a.
b.
c.
d.
11. Supplementary angles are two angles whose measures have sum ____.
Complementary angles are two angles whose measures have sum ____.
a. 90; 180
b. 90; 45
c. 180; 360
d. 180; 90
12. How are the two angles related?
71°
109°
Drawing not to scale
a. supplementary
b. vertical
c. adjacent
d. complementary
Standard MTH.PPF.451 Use several angle properties to find an unknown angle measurement
13. In the figure below, parallel lines l and m are intersected by the transversals k and t. Transversals k and t intersect at a
point on line l as shown. Based on the information given in the figure, find the measures of angles 1, 2, 3, and 4.
1
l
2
3
48°
4
m
137°
k
t
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.
14. If 8 measures 126, what is the sum of the measures of 1 and 4?
a. 252
b. 108
c. 126
15. How are
and
related?
a. alternate interior angles
b. same-side interior angles
d. 306
c. correponding angles
d. none of these
Geometry G2 HW 2
Due 9/13
Answer Section
Special Angles and Angle Relationships
1. ANS:
1,5; 2,6; 3,7; 4,8
PTS: 1
2. ANS:
1,9; 2,10
PTS: 1
3. ANS:
answer
PTS: 1
4. ANS:
answer
PTS: 1
5. ANS:
answer
PTS: 1
6. ANS: 139
PTS: 1
DIF: Bloom's Level: Comprehension
REF: Mathematics
OBJ: Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity,
reflections, symmetry, and transformations including flips, slides, turns, enlargements, rotations, and fractals.
STA: NO ALIGNMENT FOUND
TOP: Geometric Concepts, Properties, and Relationships
KEY: parallel lines | transversal | vertical angles | alternate interior angles | same side interior angles | alternate
exterior angles | same side exterior angles MSC: MA-10-00250
7. ANS: 141
PTS: 1
DIF: Bloom's Level: Comprehension
REF: Mathematics
OBJ: Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity,
reflections, symmetry, and transformations including flips, slides, turns, enlargements, rotations, and fractals.
STA: NO ALIGNMENT FOUND
TOP: Geometric Concepts, Properties, and Relationships
KEY: parallel lines | transversal | vertical angles | alternate interior angles | same side interior angles | alternate
exterior angles | same side exterior angles MSC: MA-10-00250
8. ANS: 36
PTS: 1
DIF: Bloom's Level: Comprehension
REF: Mathematics
OBJ: Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity,
reflections, symmetry, and transformations including flips, slides, turns, enlargements, rotations, and fractals.
STA: NO ALIGNMENT FOUND
TOP: Geometric Concepts, Properties, and Relationships
KEY: parallel lines | transversal | vertical angles | alternate interior angles | same side interior angles | alternate
exterior angles | same side exterior angles MSC: MA-10-00250
9. ANS:
62
10.
11.
12.
13.
PTS: 1
DIF: L2
REF: 3-1 Properties of Parallel Lines
OBJ: 3-1.2 Properties of Parallel Lines
NAT: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16
STA: CO 4.3
KEY: angle | parallel lines | transversal
MSC: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16
ANS: D
PTS: 1
DIF: L1
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Identifying Angle Pairs
NAT: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
STA: CO 4.3
TOP: 2-5 Example 1
KEY: supplementary angles
MSC: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
ANS: D
PTS: 1
DIF: L1
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Identifying Angle Pairs
NAT: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
STA: CO 4.3
TOP: 2-5 Example 1
KEY: supplementary angles | complementary angles
MSC: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
ANS: A
PTS: 1
DIF: L1
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Identifying Angle Pairs
NAT: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
STA: CO 4.3
TOP: 2-5 Example 1
KEY: supplementary angles
MSC: NAEP G3g | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.13 |
TV.LV20.14
ANS:
,
,
,
Angle 4 is an alternate interior angle of lines l and m and transversal t, so
.
To find the measure of 2, use the vertical angles property with the angel labeled 137°. Now this angle and
same side interior angles of lines l and m and transversal k, so they are supplementary. Therefore,
.
The sum of the measures of
.
Finally,
1 and
2 and
2 are
3 and 48° must be 180° since these angles form a straight line. So,
3 are vertical angles, so
.
PTS: 1
DIF: Bloom's Level: Application
REF: Mathematics
OBJ: Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity,
reflections, symmetry, and transformations including flips, slides, turns, enlargements, rotations, and fractals.
STA: NO ALIGNMENT FOUND
TOP: Geometric Concepts, Properties, and Relationships
KEY: parallel lines | transversal | vertical angles | alternate interior angles | same side interior angles | alternate
exterior angles | same side exterior angles | triangle
MSC: MA-10-00296
14. ANS: A
PTS: 1
DIF: L2
REF: 3-1 Properties of Parallel Lines
OBJ: 3-1.2 Properties of Parallel Lines
NAT: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16
STA: CO 4.3
KEY: parallel lines | transversal
MSC: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16
15. ANS: A
PTS: 1
DIF: L1
REF: 3-1 Properties of Parallel Lines
OBJ: 3-1.1 Identifying Angles
NAT: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16
STA: CO 4.3
TOP: 3-1 Example 2
KEY: parallel lines | transversal | angle
MSC: NAEP M1f | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM
| S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.16