geometry 45 to79

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2018
GEOMETRY
Congruence, Similarity,
Right Triangles, and
Trigonometry
MAFS.912.G-CO.1.1
Drag the words to the correct descriptions. Not all options will be used.
Circle
the set of points extending in one
direction in a plane
.….
Line
.
the set of points between two endpoints
in a plane
.
the set of all points the same distance
from a given point in a plane
Angle
Line Segment
Ray
.
the set of points extending in opposite
directions in a plane
MAFS.912.G-CO.1.1
Classify each statement in the table as correct or incorrect.
Select one cell per row.
Correct
If two lines in the same plane do not intersect, the lines
must be parallel.
If two line in the space do not intersect, the lines must be
parallel.
If two lines are parallel, the lines must lie in the same
plane.
Incorrect
MAFS.912.G-CO.1.1
Points ?, ?, and ? are distinct points, and ?? = ??. Which of these
statements must be true? Select all that apply.
? ?, ?, and ? are coplanar.
? ?, ?, and ? are collinear.
?
? K is the midpoint of ??.
? ?? ? ??
? The measure of ???? is 90°.
MAFS.912.G-CO.1.2
Pentagon ABCDE is shown in the ?? -coordinate plane.
Pentagon ABCDE will be rotated 90° clockwise about the
point (1, 1) to form pentagon A’B’C’D’E’.
Choose the graph that shows the correct placement of
A’B’C’D’E’ after the transformation.
A
B
C
D
MAFS.912.G-CO.1.2
Triangle ??? is shown in the ??-coordinate
plane. It will be rotated 90 degrees clockwise
about the origin to form triangle ?’?’?’.
Select the correct orientation of ?’?’?’ and
place it correctly in the coordinate plane.
MAFS.912.G-CO.1.2
A triangle is shown on the coordinate
grid.
Use the Connect Line tool to draw the
triangle after a transformation
following the rule ?, ? ? ? – 4, ? + 3
MAFS.912.G-CO.1.2
The pre-image of ?ABC and its image ?A’B’C’ are shown on the
coordinate plane.
Which rule describes the transformation
represented in the graph?
A.
1
?
2
1
2
B.
2? + 2, 2? – 3
C.
1
?
2
D.
2? – 2, 2? + 3
+ 2, ? – 3
1
2
– 2, ? + 3
MAFS.912.G-CO.1.4
A rotation about Point D maps Point ? to ?’ and Point ? to ?’.
Which statement must be true? Select
all that apply.
? ?? = ?’ ? ‘
? ?? = ?’ ?
? ???’?? = ???’??
? ???’DB’ = ???’??
? ???’?? = ???’??
? If Point ? is ?, ? , then Point ?’ is -?, ?
? If Point B is (?, ?), then Point ?’ is (?, ?)
MAFS.912.G-CO.1.4
On a coordinate plane, each point on ?? is defined by coordinates ?, ? . The segment
is rotated 90° counterclockwise to create ?’?’. Which of the following defines a point
on ?’?’ that corresponds to a point on ??.
A. ?, -?
B. -?, ?
C. ?, ?
D. -?, ?
MAFS.912.G-CO.1.3
Which figure always has exactly four lines of reflection that map the
figure onto itself?
A. square
B. rectangle
C. regular octagon
D. equilateral triangle
MAFS.912.G-CO.1.3
Select the values that correctly complete the sentence about the
symmetry of a regular pentagon.
5
A regular pentagon has _____
lines of symmetry and
1
2
5
6
72 degree
has ___________
rotational symmetry.
60 degree
72 degree
108 degree
540 degree
MAFS.912.G-CO.1.3
Trapezoid RSTU is shown.
Write the equation for the line that would map the
trapezoid onto itself.
MAFS.912.G-CO.1.5
In the diagram below, ???? ? ????.
Which sequence of transformations maps ????
onto ?????
A. a reflection over the ? -axis followed by a
translation
B. a reflection over the ? -axis followed by a
translation
C. a rotation of 180° about the origin followed
by a translation
D. a counterclockwise rotation of 90° about
the origin followed by a translation
MAFS.912.G-CO.1.5
Quadrilateral ???? is shown on the
coordinate grid.
Keisha reflects the figure across the
line ? = ? to create ?’ ? ‘ ?’ ? ‘ .
Use the Connect Line tool to draw
quadrilateral ?’ ? ‘ ?’ ? ‘ .
MAFS.912.G-CO.1.5
The right triangle in the coordinate plane is rotated 270° clockwise about the point
(2, 1) and then reflected across the ? -axis to form ? ?’ ?’ ? ‘ .
Drag and drop the appropriate orientation for triangle ?’?’?’ into the correct
position on the coordinated plane.
MAFS.912.G-CO.1.5
?ABC is shown on the coordinate plane.
After rotating ?ABC 180° about the origin and
then reflecting it over the x-axis, what are the
coordinates of ?A?B?C??
A. A?(2, 6), B?(5, 4), C?(2, 1)
B. A?(6, 2), B?(4, 5), C(1, 2)
C. A?(-2, 6), B?(5, 4), C?(-2, 1)
D. A?(6, -2), B?(4, -5), C?(1, -2)
MAFS.912.G-CO.1.5
Given quadrilateral ABCD, what are the coordinates for the resulting image,
A?B?C?D?, after the two transformations listed?
• First transformation: Rotate 90° clockwise about the origin.
• Second transformation: Translate ?, ? ? (? + 1, ? – 2).
Enter the coordinates for the resulting image
A?B?C?D? in the boxes.
A” =
B” =
C” =
D” =
MAFS.912.G-CO.1.5
Triangle EGF is graphed below.
Triangle EGF will be rotated 90° counterclockwise
around the origin and will then be reflected
across the y-axis, producing an image triangle.
Which additional transformation will map the
image triangle back onto the original triangle?
A. rotation 270° counterclockwise around the
origin
B. rotation 180° counterclockwise around the
origin
C. reflection across the line ? = – ?
D. reflection across the line ? = ?
MAFS.912.G-CO.1.5
Parallelogram ???? has midpoints ?, ?, ?, ? marked on the sides as shown.
Which rigid motion could be applied to ????
to show that ???? ? ?????
A. reflection over ??
B. reflection over ??
C. rotation 90° clockwise about the
intersection point of ?? and ??.
D. rotation 180° clockwise about the
intersection point of ?? and ??.
MAFS.912.G-CO.2.6
Triangle ??? is shown in the ??-coordinate plane. The
triangle will be rotated 180° clockwise around the point
(3, 4) to create triangle ?’?’?’. Indicate whether each of
the listed features of the image will or will not be the
same as the corresponding feature in the original
triangle by selecting the appropriate box in the table.
the
coordinates
of A’
will be the
same
will not be
the same
the
coordinates
of C’
the
perimeter
of ??’ ?’ ?’
the area
of ??’ ?’ ?’
the
measure of
?B’
the slope
of ?’ ?’
MAFS.912.G-CO.2.6
In the illustration, figure I and figure II are isosceles trapezoids.
Tran makes a conjecture that figure I is congruent to figure II.
Select each transformation or combination of transformations
that can help Tran prove his conjecture.
Select all that apply.
?
?
?
?
?
?
Rotate figure I 60° clockwise around point P.
Rotate figure I 120° clockwise around point P.
Reflect figure I across line ?, and then reflect the image across line ?.
Reflect figure I across line ?, and then reflect the image across line ?.
Rotate figure I 180° around point P, and then reflect the image across line ?.
Rotate figure I 120° counterclockwise around point P, and then reflect the
image across line ?.
MAFS.912.G-CO.2.7
All corresponding sides and angles of ? ??? and ? ??? are congruent.
Select all the statements that must be true.
? There is a reflection that maps ?? to ??.
? There is a dilation that maps ? ??? to ? ???.
? There is a translation followed by a rotation that maps ?? to ??.
? There is a sequence of rigid motions that maps ? ??? to ? ???.
? There is not necessarily a sequence of rigid motions that maps ? ??? to ? ???.
MAFS.912.G-CO.2.7
?ABC and ?DEF are plotted on the coordinate plane shown.
Which conclusions can be made about ?ABC and ?DEF if ?ABC
is mapped onto ?DEF by reflecting ?ABC over the ?-axis and
reflecting it over the ?-axis? Select all that apply.
? ?ABC ? ?DEF
? The corresponding sides are proportional:
??
??
=
??
??
=
??
??
.
? Reflecting ?ABC across the ?-axis and then the ?-axis
yields the same transformation as rotating ?ABC 90°
counterclockwise around the origin.
? ?ABC ~?DEF
? ?ABC is acute, but ?DEF is obtuse.
? All corresponding sides are congruent.
MAFS.912.G-CO.2.8
Aniyah has repeatedly stenciled the triangle
shape shown on her bedroom wall.
Her best friend, Daniela, wants to copy the exact same shape on her bedroom
wall. Which statement has sufficient information about the triangle for Aniyah to
give to Daniela to guarantee Daniela will have the exact same triangle?
A. Construct a triangle with angles whose measures are 33°, 42°, and 105°.
B. Construct a triangle with sides of measure 22 inches and 27 inches where the
included angle is 105°.
C. Construct a triangle with sides of measure 39 inches and 22 inches and a
nonincluded angle of measure 33°.
D. Construct a triangle with a 105° angle opposite from a side of length 39 inches
where the remaining two sides differ in length by 5 inches.
MAFS.912.G-CO.3.9
Quadrilateral ???? is shown.
For what value of ? will line ?? be the
perpendicular bisector of segment ???
A. 5
B. 9
C. 14
D. 17
MAFS.912.G-CO.3.9
Mikayla is using the following information to prove
that ???? and ???? are complementary angles in the
diagram shown. Part of her proof is shown below.
Given: The ray ?? bisects ???? and the ray ??
bisects ????.
Statements
Which statements could be used
to complete Mikayla’s proof?
Reasons
A.
4. 2 · m???? = 2 · m????
5. ????? = ?????
???? and ???? are
supplementary angles
TP is a line
2
????? + m???? = 180°
Definition of supplementary
angles
B.
4. 2 · m???? = 2 · m????
5. ????? + m???? = 90°
3
????? = 2 · m????
????? = 2 · m????
Property of angle bisectors
C.
4. 2 · ????S + 2 · m???? = 180°
5. ????? = ?????
D.
4. 2 · ????S + 2 · m???? = 180°
5. ????? + m???? = 90°
1
Substitution
4
Division property of equality
5
6
???? and ???? are
complementary angles
Definition of complementary
angles
MAFS.912.G-CO.3.9
In the figure shown, ?? intersects ?? and ?? at points ? and ?, respectively.
Part A
Given:???? ? ????
Prove:???? ? ????
Select from the drop-down menus to support each line
of the proof.
Statement: ???? ? ???? Reason:
Choose one…
Statement: ???? ? ???? Reason:
Choose one…
Statement: ???? ? ???? Reason:
Choose one…
MAFS.912.G-CO.3.9
In the figure shown, ?? intersects ?? and ?? at points ? and ?, respectively.
Part B
Given:m???? = ?????
Prove:m???? + ????? = 180°
Select from the drop-down menus to support each line
of the proof.
Statement: ????? = ????? Reason:
Choose one…
Statement: m???? + ????? = 180° Reason:
Choose one…
Statement: m???? + ????? = 180° Reason:
Choose one…
MAFS.912.G-CO.3.9
Given: ?? is the perpendicular bisector of ??.
Prove: J is equidistant from L and K
Statements
Reasons
?? is the perpendicular bisector of
??
Given
???? and ???? are right angles
Definition of right angle
?? ? ??
???? ? ????
???? ? ????
All right angles are congruent
?? ? ??
Definition of bisector
???? ? ????
Reflexive property of equality
Definition of right angle
???? ? ????
SAS
Definition of perpendicular
? ? ??
??
Corresponding parts of congruent
triangles are congruent
J is equidistant from L and K
Definition of equidistant
?? ? ??
Corresponding parts of congruent
triangles are congruent
MAFS.912.G-CO.3.10
Roads connecting the towns of Oceanside, River City, and Lake View form
a triangle. The distance from Oceanside to River City is 38 kilometers. The
distance from River City to Lake View is 26 kilometers. What is the
smallest possible whole number of kilometers between Lake View and
Oceanside?
Enter your answer in the box.
MAFS.912.G-CO.3.10
Which of the following sets of lengths could form the sides of a triangle?
Choose all that apply.
? 5, 9, 7
? 4, 8, 3
? 11, 11, 22
? 2, 5, 4
? 7, 9, 12
? 10, 8, 2
MAFS.912.G-CO.3.10
Complete the proof by filling in the missing
reasons from the “Reasons Bank” below.
Given: ?? ? ??
Reasons Bank
Prove: ????~????
AA Similarity Postulate
Statements
?? ? ??
?? ? ??
???? ? ????
????~????
Reasons
Given
If 2 parallel lines are cut by a
transversal, then the alternate
interior angles are congruent
Vertical angles are congruent
AA Similarity Postulate
SAS Similarity Theorem
SSS Similarity Theorem
Vertical angles are congruent
If 2 parallel lines are cut by a transversal, then
the alternate interior angles are congruent.
If 2 parallel lines are cut by a transversal, then
the corresponding angles are congruent
MAFS.912.G-CO.3.11
Parallelogram ABCD is shown.
What are the values of ? and ??
Enter the correct values in the boxes.
?=
?=
MAFS.912.G-CO.3.11
In quadrilateral ????, ?? and ?? intersect at point ?, so that ?? ? ?? and
?? is parallel to ??. Which additional information is needed to prove that
figure ???? is a rectangle?
A. ?? ? ??
B. ?? ? ??
C. ???? ? ????
D. ???? ? ????
MAFS.912.G-CO.3.11
Which set of statements would describe a parallelogram that can always
be classified as a rhombus?
I. Diagonals are perpendicular bisectors of each other.
II. Diagonals bisect the angles from which they are drawn.
III. Diagonals form four congruent isosceles right triangles.
A. I and II
B. I and III
C. II and III
D. I, II, and III
MAFS.912.G-CO.3.11
Given: Quadrilateral ???? is a parallelogram.
Prove: ?? = ?? and ?? = ??
Statements
Reasons
Quadrilateral ???? is
a parallelogram
Given
S.S.S
?? ? ??
?? ? ?? and ?? ? ??
Definition of a parallelogram
S.A.S
?? ? ??
A.S.A
?? ? ??
???? ? ????
???? ? ????
When two parallel lines are cut by a transversal,
alternate interior angles are congruent
?? ? ??
Opposite sides of a parallelogram
are congruent
When two parallel lines are cut by a transversal,
corresponding angles are congruent
???? ? ????
A.S.A
?? ? ??
?? ? ??
Corresponding parts of congruent
triangles are congruent
When two parallel lines are cut by a transversal,
same side interior angles are congruent
?? = ?? and ?? = ??
Definition of congruent segments
When two parallel lines are cut by a transversal,
alternate interior angles are congruent
MAFS.912.G-CO.3.11
Given: ABCD is a parallelogram
Prove: ?1 and ?2 are supplementary.
Proof:
It is given that ABCD is a parallelogram with angles
named, in consecutive order, ?1, ?2, ?3, and ?4.
Opposite angles of a parallelogram are congruent. Thus
m?1 = m?3 and __________
??2 = ??4
definition of congruence
__________
by the ______________.
The sum of the interior angles of any quadrilateral is
360°, so m?1 + ?2 + ?3 + ?4 = 360° .
substitution property
??1 + ??1 + ??2 + ??2 = 360°
Using the _______________,
_______________.
Therefore, 2 m?1 + ?2 = 360°
??1 + ??2 = 180°
division property
By the _______________,
_______________.
Therefore, ?1 and ?2 are supplementary.
m?1 = ??2
m?2 = ??4
m?1 = ??3
m?2 = ??3
m?1 + ??2 = 180°
m?1 + ??1 + ??2 + ??2 = 360°
m?3 + ??4 + ??3 + ??4 = 360°
Definition of congruence
Definition of equality
Division property of equality
Substitution property of equality
Transitive property of equality
MAFS.912.G-CO.3.11
The figure shows parallelogram ???? with ?? = 16.
Let ?? = ? 2 – 48 and let ?? = 2?. What are the
lengths of ?? and ???
?? =
?? =
Parallelogram ABCD is a __________________
because the ____________________.
MAFS.912.G-CO.3.11
Three vertices of parallelogram PQRS are shown:
? 8, 5 , ? 5,1 , ? 2,5
Place the statements and reasons in the table to complete the proof that shows
that parallelogram PQRS is a rhombus.
Statements
Reasons
?? = 5
Pythagorean Theorem
?? = 5
Pythagorean Theorem
?? = ??
Substitution
?? = ??
Definition of congruent lines
?? = ??
Property of a parallelogram
?? ? ??
Property of a parallelogram
Parallelogram PQRS
is a rhombus
Definition of a rhombus
?? = 5
?? = 7
?? = 5
?? = 5
?? = 7
?? = 7
???? = 90°
?? ? ??
Pythagorean
Theorem
Definition of
perpendicular lines
Property of a
parallelogram
Definition of parallel
lines
MAFS.912.G-CO.4.12
Which of the following best describes the construction?
A. ?? < ?? B. ? is the midpoint of ?. C. ?? ? ?? D. ? is the midpoint of ?. MAFS.912.G-CO.4.12 A student is working on a geometric construction. If ?? is drawn, what geometric construction is shown? A. angle bisector B. copying an angle C. perpendicular bisector D. measuring an angle MAFS.912.G-CO.4.12 The figure above shows the construction of the angle bisector of angle AOB using a compass. Which of the following statements must always be true in the construction of the angle bisector? Classify each statement in the table as correct or incorrect. Select one cell per row. Correct ?? = ?? ?? = ?? ?? = ?? ?? = ?? ?? = ?? Incorrect MAFS.912.G-CO.4.12 The figure shows line ?, points ? and ? on line ?, and point ? not on line ?. Also shown is ray ??. Part A Consider the partial construction of a line parallel to r through point Q. What would be the final step in the construction? A. B. C. D. draw draw draw draw a a a a line line line line through through through through P and S Q and S T and S Wand S Part B Once the construction is complete, which of the reasons listed contribute to proving the validity of the construction? A. When two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. B. When two lines are cut by a transversal and the verti ... Purchase answer to see full attachment

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