Download Final Review Geometry

Final Review Geometry
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which is a correct two-column proof?
Given:
Prove:
and
n
are supplementary.
p
d
l
b
c
h
j
a.
b.
c.
k
m
d. none of these
____
2.
. Find the value of x for p to be parallel to q. The diagram is not to scale.
3 4
5
1 2
6
p
q
a. 114
____
b. 126
c. 120
d. 20
c. 147
d. 75
3. Find the value of x. The diagram is not to scale.
72°
105°
a. 33
____
x°
b. 162
4. The folding chair has different settings that change the angles formed by its parts. Suppose
is 70. Find
. The diagram is not to scale.
1
2
3
a. 96
____
b. 106
c. 116
5. Find the value of x. The diagram is not to scale.
Given:
,
,
d. 86
is 26 and
S
R
a. 5
____
T
U
b. 24
c. 20
d. 40
c. pentagon
d. octagon
6. Classify the polygon by its sides.
a. triangle
b. hexagon
____
7. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is
____.
a. (n – 2)180
b. 360
c.
d. 180n
____
8. Write an equation for the horizontal line that contains point E(–3, –1).
a. x = –1
b. x = –3
c. y = –1
d. y = –3
____
9. Which two lines are parallel?
I.
II.
III.
a. I and II
b. I and III
c. II and III
d. No, two of the lines are parallel.
____ 10. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a. If a point is in the first quadrant, then its coordinates are positive.
b. If a point is not in the first quadrant, then the coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
d. If the coordinates of a point are not positive, then the point is not in the first quadrant.
____ 11. Which conditional has the same truth value as its converse?
a. If x = 7, then
.
b. If a figure is a square, then it has four sides.
c. If x – 17 = 4, then x = 21.
d. If an angle has measure 80, then it is acute.
____ 12. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible,
write not possible.
Statement 1: If x = 3, then 3x – 4 = 5.
Statement 2: x = 3
a. 3x – 4 = 5
c. If 3x – 4 = 5, then x = 3.
b. x = 3
d. not possible
____ 13. In the paper airplane,
and
D
H
A
B
Find
E
C
G
Drawing not to scale
a. 131
F
b. 49
c. 90
d. 59
____ 14. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
d°
38°
g
5
b
f°
e°
3
a. 4
4
52°
c
b. 5
____ 15. Name the angle included by the sides
c. 3
and
d. 38
N
M
P
a.
b.
c.
d. none of these
____ 16. Name the theorem or postulate that lets you immediately conclude
|
A
D
|
B
C
a. SAS
b. ASA
c. AAS
d. none of these
____ 17. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?
a. 69°
b. 84°
c. 138°
d. 96°
____ 18. Which overlapping triangles are congruent by ASA?
a.
b.
c.
d.
____ 19. Name the point of concurrency of the angle bisectors.
a. A
b. B
c. C
d. not shown
____ 20. Which diagram shows a point P an equal distance from points A, B, and C?
a.
c.
b.
d.
____ 21. For the triangle, find the coordinates of the point of concurrency of the perpendicular bisectors of the sides.
y
5
–5
5
x
–5
a. (1, 1)
b.
3 3
( ,  )
2 2
c.
1
( , 1)
2
d.
3 1
( ,  )
2 2
bisects DAB . Find ED if
____ 22. Given:
a. 51
b. 540
and
(not drawn to scale)
c. 39
d. 21
____ 23. Which of these lengths could be the sides of a triangle?
a. 15 cm, 4 cm, 20 cm
c. 11 cm, 5 cm, 16 cm
b. 3 cm, 15 cm, 20 cm
d. 5 cm, 12 cm, 16 cm
____ 24. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
____ 25. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The
diagram is not to scale.
D
E
H
G
a. x = 6, y = 3
F
b. x = 2, y = 3
c. x = 3, y = 2
____ 26. What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
Prove:
d. x = 3, y = 6
A
B
D
C
Statements
Reasons
1. Definition of parallelogram
1.
2.
3.
4.
5.
6.
2. Alternate Interior Angles Theorem
3. Definition of parallelogram
4. Alternate Interior Angles Theorem
5. Reflexive Property of Congruence
6. ?
a. Reflexive Property of Congruence
b. ASA
c. Alternate Interior Angles Theorem
d. SSS
____ 27. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.
a. x = 4, DF = 13, EG = 13
c. x = 4, DF = 15, EG = 15
b. x = 4, DF = 15, EG = 18
d. x = 2, DF = 13, EG = 13
____ 28. Find
in the kite. The diagram is not to scale.
|
3
1
2
B
||
||
D
39°
|
A
C
a. 51, 51
b. 39, 39
c. 39, 51
____ 29. Name the set(s) of numbers to which –5 belongs.
a. whole numbers, natural numbers, integers
b. rational numbers
c. whole numbers, integers, rational numbers
d. integers, rational numbers
Complete the statement with , , or =.
____ 30.
d. 51, 39
a.
b.
c. =
Short Answer
31. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
32. The 8 rowers in the racing boat stroke so that the angles formed by their oars with the side of the boat all stay
equal. Explain why their oars on either side of the boat remain parallel.
33. Identify the form of the equation –3x – y = –2. To graph the equation, would you use the given form or
change to another form? Explain.
34. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof.
Given:
Prove:
B
C
A
D
35. In the figure,
,
, and
. Prove that
.
36. Can these three segments form the sides of a triangle? Explain.
c
b
a
In the diagram,
are midsegments of triangle ABC. Find the value of the variable if
.
37. z
38. What type of quadrilateral has exactly one pair of parallel sides?
39. The fact that the diagonals of a kite are perpendicular suggests a way to place a kite in the coordinate plane.
Show this placement. Include labels for the kite vertices.
Approximate the square root to the nearest whole number.
40.
Essay
41. Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line, then they
are parallel to each other.
Given:
Prove:
s
1
2
3
4
5
6
7
8
r
t
42. Write a two-column proof.
Given:
Prove:
are supplementary.
1
2
3
l
4
5
6
7
8
m
43. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
o
31
x
w
v
y
o
68
z
44. Given:
are complementary, and
are complementary.
Prove:
Other
45. Is each figure a polygon? If yes, describe it as concave or convex and classify it by its sides. If not, tell why.
a.
b.
c.
46. Line p contains points A(–1, 4) and B(3, –5). Line q is parallel to line p. Line r is perpendicular to line q.
What is the slope of line r? Explain.
47. When you open a stepladder, you use a brace on each side of the ladder to lock the legs in place. Explain why
the triangles formed on each side by the legs and the ground (
in the diagram) are
congruent.
48. A tennis court has a baseline at each end. One is labeled in the picture. Which part of the tennis court is
equidistant from the midpoints of the two baselines? Explain.
Final Review Geometry
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
KEY:
2. ANS:
REF:
OBJ:
NAT:
KEY:
3. ANS:
REF:
OBJ:
NAT:
TOP:
4. ANS:
REF:
OBJ:
NAT:
TOP:
5. ANS:
REF:
OBJ:
NAT:
KEY:
6. ANS:
REF:
NAT:
TOP:
7. ANS:
REF:
NAT:
KEY:
8. ANS:
OBJ:
NAT:
TOP:
9. ANS:
REF:
NAT:
TOP:
10. ANS:
OBJ:
TOP:
11. ANS:
A
PTS: 1
DIF: L2
REF: 3-1 Properties of Parallel Lines
3-1.2 Properties of Parallel Lines
NAT: NAEP 2005 M1f | ADP K.2.1
3-1 Example 3
proof | two-column proof | supplementary angles | parallel lines | reasoning
D
PTS: 1
DIF: L2
3-3 Parallel and Perpendicular Lines
3-3.1 Relating Parallel and Perpendicular Lines
NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1
TOP: 3-3 Example 2
parallel lines
A
PTS: 1
DIF: L2
3-4 Parallel Lines and the Triangle Angle-Sum Theorem
3-4.2 Using Exterior Angles of Triangles
NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
3-4 Example 3
KEY: triangle | sum of angles of a triangle
A
PTS: 1
DIF: L2
3-4 Parallel Lines and the Triangle Angle-Sum Theorem
3-4.2 Using Exterior Angles of Triangles
NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
3-4 Example 4
KEY: triangle | sum of angles of a triangle
D
PTS: 1
DIF: L3
3-4 Parallel Lines and the Triangle Angle-Sum Theorem
3-4.2 Using Exterior Angles of Triangles
NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
exterior angle
B
PTS: 1
DIF: L2
3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.1 Classifying Polygons
NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
3-5 Example 2
KEY: classifying polygons
B
PTS: 1
DIF: L2
3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
Polygon Exterior Angle-Sum Theorem
C
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
3-6 Example 6
KEY: vertical line
A
PTS: 1
DIF: L2
3-7 Slopes of Parallel and Perpendicular Lines
OBJ: 3-7.1 Slope and Parallel Lines
NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
3-7 Example 2
KEY: slopes of parallel lines | parallel lines
C
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.2 Converses
NAT: NAEP 2005 G5a
2-1 Example 5
KEY: conditional statement | coverse of a conditional
C
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
OBJ:
TOP:
KEY:
ANS:
OBJ:
KEY:
ANS:
OBJ:
TOP:
ANS:
OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
ANS:
REF:
OBJ:
NAT:
KEY:
ANS:
REF:
OBJ:
TOP:
KEY:
ANS:
REF:
NAT:
KEY:
ANS:
REF:
NAT:
KEY:
ANS:
LOC:
TOP:
KEY:
NOT:
ANS:
NAT:
KEY:
ANS:
TOP:
MSC:
ANS:
2-1.2 Converses
NAT: NAEP 2005 G5a
2-1 Example 6
conditional statement | coverse of a conditional | truth value
A
PTS: 1
DIF: L4
REF: 2-3 Deductive Reasoning
2-3.1 Using the Law of Detachment
NAT: NAEP 2005 G5a
Law of Detachment | deductive reasoning
B
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Congruent Figures
NAT: NAEP 2005 G2e | ADP K.3
4-1 Example 2
KEY: congruent figures | corresponding parts
C
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Congruent Figures
NAT: NAEP 2005 G2e | ADP K.3
4-1 Example 1
KEY: congruent figures | corresponding parts
A
PTS: 1
DIF: L2
4-2 Triangle Congruence by SSS and SAS
4-2.1 Using the SSS and SAS Postulates
NAT: NAEP 2005 G2e | ADP K.3
4-2 Example 2
KEY: angle
A
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem
NAT: NAEP 2005 G2e | ADP K.3
4-3 Example 3
KEY: ASA | AAS | SAS
D
PTS: 1
DIF: L2
4-5 Isosceles and Equilateral Triangles
4-5.1 The Isosceles Triangle Theorems
NAEP 2005 G3f | ADP J.5.1 | ADP K.3
TOP: 4-5 Example 2
isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
A
PTS: 1
DIF: L3
4-7 Using Corresponding Parts of Congruent Triangles
4-7.1 Using Overlapping Triangles in Proofs
NAT: NAEP 2005 G3f | ADP K.3
4-7 Example 2
congruent figures | corresponding parts | overlapping triangles | proof
C
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
NAEP 2005 G3b
angle bisector | incenter of the triangle | point of concurrency
A
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.1 Properties of Bisectors
NAEP 2005 G3b
TOP: 5-3 Example 2
circumcenter of the triangle | circumscribe
A
PTS: 1
DIF: Level B
REF: MHGM0087
NCTM.PSSM.00.MTH.9-12.GEO.2.a
Lesson 5.2 Use Perpendicular Bisectors
triangle | perpendicular bisector | concurrency
MSC: Knowledge
978-0-547-31534-8
C
PTS: 1
DIF: Level B
REF: PHGM0420
NT.CCSS.MTH.10.9-12.G-SRT.8 TOP: Lesson 5.3 Use Angle Bisectors of Triangles
solve | angle bisector
MSC: Application NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level B
REF: PHGM0418
Lesson 5.5 Use Inequalities in a Triangle
KEY: triangle inequality
Comprehension
NOT: 978-0-547-31534-8
C
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
25.
26.
27.
28.
29.
30.
OBJ:
KEY:
ANS:
OBJ:
TOP:
KEY:
ANS:
OBJ:
KEY:
ANS:
OBJ:
TOP:
ANS:
OBJ:
TOP:
ANS:
OBJ:
NAT:
TOP:
ANS:
TOP:
KEY:
6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals
C
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.2 Properties: Diagonals and Transversals
NAT: NAEP 2005 G3f
6-2 Example 3
transversal | diagonal | parallelogram | Theorem 6-3 | algebra
B
PTS: 1
DIF: L3
REF: 6-2 Properties of Parallelograms
6-2.2 Properties: Diagonals and Transversals
NAT: NAEP 2005 G3f
proof | two-column proof | parallelogram | diagonal
C
PTS: 1
DIF: L2
REF: 6-4 Special Parallelograms
6-4.1 Diagonals of Rhombuses and Rectangles
NAT: NAEP 2005 G3f
6-4 Example 2
KEY: rectangle | algebra | Theorem 6-11 | diagonal
C
PTS: 1
DIF: L2
REF: 6-5 Trapezoids and Kites
6-5.1 Properties of Trapezoids and Kites
NAT: NAEP 2005 G3f
6-5 Example 3
KEY: kite | Theorem 6-17 | diagonal
D
PTS: 1
DIF: L2
REF: 1-3 Exploring Real Numbers
1-3.1 Classifying Numbers
NAEP 2005 N1d | NAEP 2005 N1g | NAEP 2005 N1j | ADP I.2.1 | ADP I.2.2 | ADP I.3
1-3 Example 1
KEY: integers | rational numbers
B
PTS: 1
DIF: Level B
REF: MLC30521
Lesson 9.2 Rational and Irrational Numbers
irrational numbers | rational numbers | compare | order
NOT: 978-0-618-73965-3
SHORT ANSWER
31. ANS:
a. Corresponding angles.
b. Vertical angles.
c. Transitive Property.
PTS: 1
DIF: L2
REF: 3-1 Properties of Parallel Lines
OBJ: 3-1.2 Properties of Parallel Lines
NAT: NAEP 2005 M1f | ADP K.2.1
TOP: 3-1 Example 3
KEY: alternate interior angles | Alternate Interior Angles Theorem | proof | reasoning | two-column proof |
multi-part question
32. ANS:
The rowers keep corresponding angles congruent.
PTS: 1
DIF: L3
REF: 3-2 Proving Lines Parallel
OBJ: 3-2.1 Using a Transversal
NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3
TOP: 3-2 Example 1
KEY: transversal | word problem | reasoning | parallel lines
33. ANS:
Standard form. Answer may vary. Sample: You could use the given form. Find the intercepts and use them to
draw the line.
PTS:
OBJ:
NAT:
KEY:
1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
graphing | point-slope form | standard form of a linear equation | slope-intercept form | writing in math
34. ANS:
Answers may vary. Sample: Since the two triangles share the side
by CPCTC.
, they are congruent by SAS. Then
PTS: 1
DIF: L2
REF: 4-4 Using Congruent Triangles: CPCTC
OBJ: 4-4.1 Proving Parts of Triangles Congruent
NAT: NAEP 2005 G2e | ADP K.3
TOP: 4-4 Example 2
KEY: SAS | CPCTC | writing in math | reasoning
35. ANS:
Answers may vary. Sample:
by SAS, so
. Supplements of congruent angles are
congruent, so
.
by AAS.
PTS: 1
DIF: L4
REF: 4-7 Using Corresponding Parts of Congruent Triangles
OBJ: 4-7.1 Using Overlapping Triangles in Proofs
NAT: NAEP 2005 G3f | ADP K.3
KEY: overlapping triangles | proof | AAS
36. ANS:
No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater
than the length of the third segment.
PTS: 1
DIF: L3
REF: 5-5 Inequalities in Triangles
OBJ: 5-5.2 Inequalities Involving Sides of Triangles
NAT: NAEP 2005 G3f
KEY: Triangle Inequality Theorem
37. ANS:
15
PTS: 1
DIF: Level B
REF: 7f580833-cdbb-11db-b502-0011258082f7
TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof
KEY: Midsegment theorem
MSC: Knowledge NOT: 978-0-547-31534-8
38. ANS:
trapezoid
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
OBJ: 6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
KEY: quadrilateral | reasoning | algebra | trapezoid | rhombus | square | parallelogram
39. ANS:
Answers may vary. Sample:
y
(0, c)
(–a, 0)
(b, 0)
x
(0, –c)
PTS: 1
DIF: L3
OBJ: 6-6.1 Naming Coordinates
KEY: kite | algebra | coordinate plane
REF: 6-6 Placing Figures in the Coordinate Plane
NAT: NAEP 2005 G4d
40. ANS:
11
PTS: 1
DIF: Level B
TOP: Lesson 9.1 Square Roots
MSC: Comprehension
REF: MLC30508 NAT: NT.CCSS.MTH.10.8.8.EE.2
KEY: square roots | approximate
NOT: 978-0-618-73965-3
ESSAY
41. ANS:
[4]
[3]
[2]
[1]
PTS:
OBJ:
NAT:
KEY:
42. ANS:
[4]
[3]
[2]
[1]
PTS:
OBJ:
KEY:
angles
43. ANS:
[4]
[3]
[2]
[1]
By the definition of , r  s implies m2 = 90, and t  s implies m6 = 90. Line s
is a transversal. 2 and 6 are corresponding angles. By the Converse of the
Corresponding Angles Postulate, r || t.
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
1
DIF: L4
REF: 3-3 Parallel and Perpendicular Lines
3-3.1 Relating Parallel and Perpendicular Lines
NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1
TOP: 3-3 Example 2
paragraph proof | proof | reasoning | extended response | rubric-based question | perpendicular lines
correct idea, some details inaccurate
correct idea, some statements missing
correct idea, several steps omitted
1
DIF: L4
REF: 3-2 Proving Lines Parallel
3-2.1 Using a Transversal
NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3
two-column proof | proof | extended response | rubric-based question | parallel lines | supplementary
w + 31 + 90 = 180, so w = 59º. Since vertical angles are congruent, y = 59º. Since
supplementary angles have measures with sum 180, x = v = 121º. z + 68 + y = z
+ 68 + 59 = 180, so z = 53º.
small error leading to one incorrect answer
three correct answers, work shown
two correct answers, work shown
PTS: 1
DIF: L3
REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem
OBJ: 3-4.2 Using Exterior Angles of Triangles
NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
KEY: Triangle Angle-Sum Theorem | vertical angles | supplementary angles | extended response |
rubric-based question
44. ANS:
[4] By the definition of complementary angles,
and
.
By the Transitive Property of Equality (or Substitution Property),
. By the Subtraction Property of Equality,
, and
by the definition of congruent angles.
OR
equivalent explanation
[3] one step missing OR one incorrect justification
[2] two steps missing OR two incorrect justifications
[1] correct steps with no explanations
PTS: 1
DIF: L4
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Theorems About Angles
NAT: NAEP 2005 G3g | ADP K.1.1
KEY: complementary angles | Properties of Equality | rubric-based question | extended response | proof
OTHER
45. ANS:
a. concave hexagon
b. concave dodecagon
c. not a polygon; two sides intersect between endpoints
PTS: 1
DIF: L3
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.1 Classifying Polygons
NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2
KEY: classifying polygons | convex | concave | writing in math
46. ANS:
4
; Line r is perpendicular to line p because a line perpendicular to one of two parallel lines is also
9
perpendicular to the other. Thus, the slope of line r is the opposite reciprocal of the slope of line p.
PTS: 1
DIF: L3
REF: 3-7 Slopes of Parallel and Perpendicular Lines
OBJ: 3-7.2 Slope and Perpendicular Lines
NAT: NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
KEY: perpendicular lines | parallel lines | slopes of parallel lines | slopes of perpendicular lines | reasoning |
writing in math
47. ANS:
Answers may vary. Sample: Each leg on one side of the ladder is the same length as the corresponding leg on
the other side. The locking braces hold the legs apart by the same angle measure. The triangles are congruent
by SAS.
PTS: 1
DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Using the SSS and SAS Postulates
NAT: NAEP 2005 G2e | ADP K.3
KEY: SAS | word problem | problem solving | writing in math
48. ANS:
The net; the net is the perpendicular bisector of the segment joining the midpoints of the two baselines. By the
Perpendicular Bisector Theorem, any point on the net is equidistant from the midpoints of the two baselines.
PTS:
OBJ:
TOP:
KEY:
1
DIF: L2
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
NAT: NAEP 2005 G3b | ADP K.2.2
5-2 Example 1
Perpendicular Bisector Theorem | perpendicular bisector | reasoning | writing in math