Lesson 1.1 ⢠Building Blocks of Geometry
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DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 1
Lesson 1.1 • Building Blocks of Geometry Name
Period
Date
3 cm. For Exercises 1–7, complete each statement. PS
P N
is ________________. 1. The midpoint of PQ
Q S
2. NQ ________________.
is ________________. 3. Another name for NS
. 4. S is the ________________ of SQ 5. P is the midpoint of ________________.
________________. 6. NS
is ________________. 7. Another name for SN 8. Name all pairs of congruent segments in KLMN. Use the
N 8 cm
congruence symbol to write your answer. K
O
M 8 cm
L
For Exercises 9 and 10, use a ruler to draw each figure. Label the figure and mark the congruent parts. and CD with M as the midpoint 9. AB and CD . AB 6.4 cm of both AB and CD 4.0 cm. A, B, and C are not collinear.
11. Sketch six points A, B, C, D, E, and F, no
three of which are collinear. Name the lines defined by these points. How many lines are there?
. C is the midpoint of AB , with and CD 10. AB
, is the AC 1.5 cm. D, not on AB midpoint of AE , with AD 2BC.
12. In the figure below, {B, C, H, E} is a set of
four coplanar points. Name two other sets of four coplanar points. How many sets of four coplanar points are there? B
C
A
D F
E
G H
Cube
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
CHAPTER 1
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Lesson 1.2 • Poolroom Math Name
Period
Date
For Exercises 1–5, use the figure at right to complete each statement.
B
1. A is the ________________ of BAE.
C
is the ________________ of BAE. 2. AD
A
D
is a ________________ of DAE. 3. AD 4. If mBAC 42°, then mCAE ________________. E
5. DAB ________________.
O
For Exercises 6–9, use your protractor to find the measure of each angle to the nearest degree. 6. mPRO
7. mORT
8. mO
9. mRTO
P R
T
A
For Exercises 10–12, use your protractor to draw and then label each angle with the given measure. 10. mMNO 15°
11. mRIG 90°
12. mz 160°
For Exercises 13–15, find the measure of the angle formed by the hands at each time. 13. 3:00
11
12
1 2
10
14. 4:00 9
3 4
8
For Exercises 15 and 16, mark each figure with all the given information.
7
6
5
15. mADB 90°, AD BD, DAB DBA B
A
D
C
16. mRPQ 90°, QR TZ, RT QZ, Q T R
Q
2
P
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Z
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
11/1/06
10:15 AM
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Lesson 1.3 • What’s a Widget? Name
Period
Date
For Exercises 1–9, match each term with one of the items (a to i) below. 2
a.
b.
?
c.
? 90°
1
d.
e.
f. ?
?
g.
h.
i.
P
?
Q R
1. _____ Vertical angles
2. _____ Obtuse angle
3. _____ Right angle
4. _____ Complementary angles
5. _____ Congruent angles
6. _____ Linear pair of angles
7. _____ Bisected angle
8. _____ Perpendicular lines
9. _____ Congruent segments 10. If mP 13°, mQ 77°, and Q and R are complementary, what
can you conclude about P and R? Explain your reasoning.
For Exercises 11–12, sketch, label, and mark a figure showing each property. 11. 1 2, 2 3
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PR 12. PQ
CHAPTER 1
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DG4PS_893_01.qxd
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Lesson 1.4 • Polygons Name
Period
Date
For Exercises 1–8, complete the table. Polygon name
Number of sides
Number of diagonals
1. Triangle
2
2.
5
3. 4. Hexagon 5. Heptagon
8
6.
35
7.
12
8.
For Exercises 9 and 10, sketch and label each figure. Mark the congruences. 9. Concave pentagon PENTA, with external
10. Equilateral quadrilateral QUAD, with
, and TA PE . diagonal ET
Q U.
For Exercises 11–14, sketch and use hexagon ABCDEF. 11. Name the diagonals from A. 12. Name a pair of consecutive sides. 13. Name a pair of consecutive angles. 14. Name a pair of non-intersecting diagonals.
For Exercises 15–18, use the figures at right. MNOPQ RSTUV
T
O
61° U
15. mN _____
16.1
16. VR _____ 17. mP _____ 18. ON _____
V Q P
8.4 7.2 M
N
82°
S
58°
R
19. The perimeter of a regular pentagon is 31 cm. Find the length of
each side.
4
CHAPTER 1
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
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Lesson 1.5 • Triangles Name
Period
Date
For Exercises 1–5, use the figure at right. Name a pair of 1. Parallel segments
B
A
2. Perpendicular segments 3. Congruent segments
C
D
E
F
4. Supplementary angles 5. Linear angles
G
H
I
For Exercises 6 and 7, sketch, label, and mark each figure. 6. Isosceles obtuse triangle TRI with vertex angle T.
, CA , 7. Scalene right triangle SCA with midpoints L, M, and N on SC , respectively. and SA
For Exercises 8 and 9, use your geometry tools to draw each figure. 8. Acute isosceles triangle ACD with vertex
9. Scalene right triangle RGH.
angle A measuring 40°.
For Exercises 10–12, use the graph at right.
y
10. Locate F so that ABF is a right triangle.
C (8, 3)
11. Locate D so that ABD is an isosceles triangle. 12. Locate G so that ABG is scalene and not a right triangle.
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
A (0, 0)
B (8, 0)
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Lesson 1.6 • Special Quadrilaterals Name
Period
Date
For Exercises 1–5, sketch, label, and mark each figure. 1. Parallelogram PGRA
2. Square SQRE
3. Rhombus RHOM with acute H.
AP , RE PA , 4. Trapezoid TRAP with TR and P, E, and A collinear.
5. Kite KITE with EK KI and obtuse K.
For Exercises 6–9, name each polygon in the figure. Assume that the grid is square.
H
J I
G
6. Square 8. Rhombus
For Exercises 10–12, use the graph at right.
7. Parallelogram
D
9. Kite
A
E B
F
C
y
10. Locate D so that ABCD is a rectangle. C (8, 3)
11. Locate E so that ABCE is a trapezoid. 12. Locate G so that points A, B, C, and G
A (0, 0)
B (8, 0)
x
determine a parallelogram that is not a rectangle.
6
CHAPTER 1
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
11/1/06
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Lesson 1.8 • Space Geometry Name
Period
Date
For Exercises 1 and 2, draw each figure. 1. A prism with a rectangular base.
2. A cylinder with base diameter greater
than height.
For Exercises 3 and 4, sketch the three-dimensional figure formed by folding each net into a solid. Name the solid. 3.
4.
For Exercises 5 and 6, sketch the section formed when each solid is sliced by the plane as shown. 5.
6.
7. Find the lengths of x and y. 3 4
2 y x
8
CHAPTER 1
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Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
11/1/06
10:15 AM
Page 1
Lesson 1.1 • Building Blocks of Geometry Name
Period
Date
3 cm. For Exercises 1–7, complete each statement. PS
P N
is ________________. 1. The midpoint of PQ
Q S
2. NQ ________________.
is ________________. 3. Another name for NS
. 4. S is the ________________ of SQ 5. P is the midpoint of ________________.
________________. 6. NS
is ________________. 7. Another name for SN 8. Name all pairs of congruent segments in KLMN. Use the
N 8 cm
congruence symbol to write your answer. K
O
M 8 cm
L
For Exercises 9 and 10, use a ruler to draw each figure. Label the figure and mark the congruent parts. and CD with M as the midpoint 9. AB and CD . AB 6.4 cm of both AB and CD 4.0 cm. A, B, and C are not collinear.
11. Sketch six points A, B, C, D, E, and F, no
three of which are collinear. Name the lines defined by these points. How many lines are there?
. C is the midpoint of AB , with and CD 10. AB
, is the AC 1.5 cm. D, not on AB midpoint of AE , with AD 2BC.
12. In the figure below, {B, C, H, E} is a set of
four coplanar points. Name two other sets of four coplanar points. How many sets of four coplanar points are there? B
C
A
D F
E
G H
Cube
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
CHAPTER 1
1
DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 2
Lesson 1.2 • Poolroom Math Name
Period
Date
For Exercises 1–5, use the figure at right to complete each statement.
B
1. A is the ________________ of BAE.
C
is the ________________ of BAE. 2. AD
A
D
is a ________________ of DAE. 3. AD 4. If mBAC 42°, then mCAE ________________. E
5. DAB ________________.
O
For Exercises 6–9, use your protractor to find the measure of each angle to the nearest degree. 6. mPRO
7. mORT
8. mO
9. mRTO
P R
T
A
For Exercises 10–12, use your protractor to draw and then label each angle with the given measure. 10. mMNO 15°
11. mRIG 90°
12. mz 160°
For Exercises 13–15, find the measure of the angle formed by the hands at each time. 13. 3:00
11
12
1 2
10
14. 4:00 9
3 4
8
For Exercises 15 and 16, mark each figure with all the given information.
7
6
5
15. mADB 90°, AD BD, DAB DBA B
A
D
C
16. mRPQ 90°, QR TZ, RT QZ, Q T R
Q
2
P
CHAPTER 1
T
Z
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 3
Lesson 1.3 • What’s a Widget? Name
Period
Date
For Exercises 1–9, match each term with one of the items (a to i) below. 2
a.
b.
?
c.
? 90°
1
d.
e.
f. ?
?
g.
h.
i.
P
?
Q R
1. _____ Vertical angles
2. _____ Obtuse angle
3. _____ Right angle
4. _____ Complementary angles
5. _____ Congruent angles
6. _____ Linear pair of angles
7. _____ Bisected angle
8. _____ Perpendicular lines
9. _____ Congruent segments 10. If mP 13°, mQ 77°, and Q and R are complementary, what
can you conclude about P and R? Explain your reasoning.
For Exercises 11–12, sketch, label, and mark a figure showing each property. 11. 1 2, 2 3
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
PR 12. PQ
CHAPTER 1
3
DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 4
Lesson 1.4 • Polygons Name
Period
Date
For Exercises 1–8, complete the table. Polygon name
Number of sides
Number of diagonals
1. Triangle
2
2.
5
3. 4. Hexagon 5. Heptagon
8
6.
35
7.
12
8.
For Exercises 9 and 10, sketch and label each figure. Mark the congruences. 9. Concave pentagon PENTA, with external
10. Equilateral quadrilateral QUAD, with
, and TA PE . diagonal ET
Q U.
For Exercises 11–14, sketch and use hexagon ABCDEF. 11. Name the diagonals from A. 12. Name a pair of consecutive sides. 13. Name a pair of consecutive angles. 14. Name a pair of non-intersecting diagonals.
For Exercises 15–18, use the figures at right. MNOPQ RSTUV
T
O
61° U
15. mN _____
16.1
16. VR _____ 17. mP _____ 18. ON _____
V Q P
8.4 7.2 M
N
82°
S
58°
R
19. The perimeter of a regular pentagon is 31 cm. Find the length of
each side.
4
CHAPTER 1
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 5
Lesson 1.5 • Triangles Name
Period
Date
For Exercises 1–5, use the figure at right. Name a pair of 1. Parallel segments
B
A
2. Perpendicular segments 3. Congruent segments
C
D
E
F
4. Supplementary angles 5. Linear angles
G
H
I
For Exercises 6 and 7, sketch, label, and mark each figure. 6. Isosceles obtuse triangle TRI with vertex angle T.
, CA , 7. Scalene right triangle SCA with midpoints L, M, and N on SC , respectively. and SA
For Exercises 8 and 9, use your geometry tools to draw each figure. 8. Acute isosceles triangle ACD with vertex
9. Scalene right triangle RGH.
angle A measuring 40°.
For Exercises 10–12, use the graph at right.
y
10. Locate F so that ABF is a right triangle.
C (8, 3)
11. Locate D so that ABD is an isosceles triangle. 12. Locate G so that ABG is scalene and not a right triangle.
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
A (0, 0)
B (8, 0)
CHAPTER 1
x
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DG4PS_893_01.qxd
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Lesson 1.6 • Special Quadrilaterals Name
Period
Date
For Exercises 1–5, sketch, label, and mark each figure. 1. Parallelogram PGRA
2. Square SQRE
3. Rhombus RHOM with acute H.
AP , RE PA , 4. Trapezoid TRAP with TR and P, E, and A collinear.
5. Kite KITE with EK KI and obtuse K.
For Exercises 6–9, name each polygon in the figure. Assume that the grid is square.
H
J I
G
6. Square 8. Rhombus
For Exercises 10–12, use the graph at right.
7. Parallelogram
D
9. Kite
A
E B
F
C
y
10. Locate D so that ABCD is a rectangle. C (8, 3)
11. Locate E so that ABCE is a trapezoid. 12. Locate G so that points A, B, C, and G
A (0, 0)
B (8, 0)
x
determine a parallelogram that is not a rectangle.
6
CHAPTER 1
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
DG4PS_893_01.qxd
11/1/06
10:15 AM
Page 8
Lesson 1.8 • Space Geometry Name
Period
Date
For Exercises 1 and 2, draw each figure. 1. A prism with a rectangular base.
2. A cylinder with base diameter greater
than height.
For Exercises 3 and 4, sketch the three-dimensional figure formed by folding each net into a solid. Name the solid. 3.
4.
For Exercises 5 and 6, sketch the section formed when each solid is sliced by the plane as shown. 5.
6.
7. Find the lengths of x and y. 3 4
2 y x
8
CHAPTER 1
4
Discovering Geometry Practice Your Skills ©2008 Key Curriculum Press
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