Download 12 Aug 9:50 - 11:20 Geometry -

12 Aug 9:50 - 11:20
Geometry Go over Part 2 of Introductory Activity
Collect Signature page-Pick up Textbook
Check Vocabulary - how useful was your
reference?
Practice Exercises
Transformational Geometry - Translations
2. Brian is correct. Every square is also a
rectangle. A rectangle is defined as a
quadrilateral with four right angles and since a
square is a quadrilateral which has four right
angles it can also be called a rectangle. Brian
made a convincing argument because he
clearly explained how the familiar definition
of a rectangle also applies to a square.
2. Brian is correct. Every square is also a
rectangle. A rectangle is defined as a
quadrilateral with four right angles and since a
square is a quadrilateral which has four right
angles it can also be called a rectangle. Brian
made a convincing argument because he
clearly explained how the familiar definition
of a rectangle also applies to a square.
Is every rectangle also a square?
3. Consider the following set of figures on a
coordinate plane.
a. Which of the following figures are
parallelograms? How do you know? A
parallelogram is a quadrilateral (4 sides) both pairs of opposite sides are parallel
and same length (congruent); diagonals
bisect. Parallel sides will have same slope.
Check our definition in Part 1.
3. Consider the following set of figures on a
coordinate plane.
a. Which of the following figures are
parallelograms? How do you know?
ABCD, EFGH, IJKL, MNOP, and QRST are all
parallelograms. I know because they all have two
pairs of parallel sides which is the definition of a
parallelogram. I can tell the sides are parallel
when they have the same slope (rise/run).
3. Consider the following set of figures on a
coordinate plane.
a. Which of the following figures are
parallelograms? How do you know?
UVWX is not a parallelogram because the slope
of UX is 3 and the slope of VW is 4, so these
sides are not parallel.
(Parallel lines remember have the same slope)
3.b. Can you identify all of the parallelograms?
Write an argument that would convince a skeptic
that you have found all of the parallelograms in
this figure.
ABCD is a parallelogram because the slope of AD
is the same as the slope of BC (no slope, 0,
horizontal line segments). The slope of AB is the
same as the slope of DC (slope = 3/2). Hence
ABCD is a quadrilateral with both pairs of
opposite sides that are parallel, a parallelogram.
3.c. Could you classify any of the parallelograms
as another type of mathematical shape? If so,
which ones? If not, why not?
3.c. Could you classify any of the parallelograms
as another type of mathematical shape? If so,
which ones? If not, why not?
IJKL is a square because the slope of IJ=slope of
KL = -2 and the slope of JK = slope of IL= ½ . -2
and ½ are opposite reciprocals , so KL is
perpendicular to JK, which means they are at
right angles (90°).
3.c. Could you classify any of the parallelograms
as another type of mathematical shape? If so,
which ones? If not, why not?
QRST is a rectangle
MNOP is a rhombus
UVWZ is a kite
4. Martin said “Quadrilateral ABCD is a rhombus
because AB||DC and AD||BC and it doesn’t have
any right angles.”
|| parallel
Simone said: “Quadrilateral ABCD is a rhombus
because it has two pairs of parallel sides and
AB=BC=CD=DA.”
4. Martin said “Quadrilateral ABCD is a rhombus
because AB||DC and AD||BC and it doesn’t have
any right angles.”
(the fact that there aren’t any right angles is not
relevant to the argument that this shape is a
rhombus. A square does have right angles, and it
is also a rhombus.
Simone said: “Quadrilateral ABCD is a rhombus
because it has two pairs of parallel sides and
4.
Simone said: “Quadrilateral ABCD is a rhombus
because it has two pairs of parallel sides and
AB=BC=CD=DA.”
This is the better argument since it mentions that
a rhombus has 2 pairs of parallel sides and also
that all 4 sides are congruent.
4.
Simone said: “Quadrilateral ABCD is a rhombus
because it has two pairs of parallel sides and
AB=BC=CD=DA.”
A more precise mathematical argument might
include naming the parallel sides. AB||DC and
AD||BC.
(Could also state the slopes of the parallel sides(3
and ⅓)
Bring up signature page and sign for textbook.
Find vocabulary in textbook, add page reference
and make sure what you have matches what the
textbook says (reliable source).
Continue to complete the table.
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
1) Plot a point, C, on rayAB so that AC<AB.
(Distance from A to C is less than distance
from A to B.)
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
2) Draw line segment DE so that it intersects
(crosses) line FG at H, and so that angle DHF is
obtuse (greater than 90 degrees).
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
3) Draw two supplementary angles, angle IJK and
angle LJK (measure of the two angles adds up to
180 degrees).
What type of angle is angle IJL?
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
3) Draw two supplementary angles, angle IJK and
angle LJK (measure of the two angles adds up to
180 degrees).
What type of angle is angle IJL? A straight angle.
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
4) Draw a triangle MNP so that angle MNP is a
right angle.
Angle NPM and angle PMN are _______ angles.
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
4) Draw a triangle MNP so that angle MNP is a
right angle.
Angle NPM and angle PMN are acute angles.
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
5) Draw line p, line q, line r and line s so that p is
parallel to q, r is parallel to s and p is
perpendicular to r.
What type of quadrilateral appears to be formed
by your lines?
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
5) Draw line p, line q, line r and line s so that p is
parallel to q, r is parallel to s and p is
perpendicular to r.
What type of quadrilateral appears to be formed
by your lines? rectangle
Practice Exercises.
Draw a picture that represents what is described
in the following problems.
6) Draw triangle TUV so that it shares a side with
quadrilateral UVWX.
Practice Exercises.
Describe 3 characteristics that appear to be true
in the drawing. Use appropriate notation and
vocabulary.
Transformational Geometry Translations
A transformation is a change in
the position, size, or shape of a
figure.
A translation is a
transformation which moves
each point of a figure the same
distance and in the same
direction.
Example 1.
△ABC is translated 1 unit right
and 4 units up. Draw the image
△A’B’C’. This would be
represented by T1,4
Example 1.
What are the coordinates of
A (1, -3)
A’
B (3, 0)
B’
C (4, -2)
C’
Example 1.
What are the coordinates of
A (1, -3)
A’ (2, 1)
B (3, 0)
B’ (4, 4)
C (4, -2)
C’ (5, 2)
Example 2.
Example 2. T-4, 5
What are the coordinates of:
J (0, 2)
J’ (-4, 7)
K (3, 4)
K’ (-1, 9)
L (5, 1)
L’ (1, 6)