PowerPoint presentation about modern geometry

Classroom Rules
1. Show respect for the teacher, classmates and
yourself.
2. Raise your hand if you want to speak/recite.
3. Do not talk when you are not called.
4. Stand when you are asked to answer.
5. Cooperate with your groups when making activities.

Mechanics:
1.The teacher will give you a puzzle consists of various pieces that,
when correctly assembled, form a shape or pattern.
2.Players begin by selecting a puzzle piece and placing it in the
correct position on the puzzle board.
3.As players place each piece, they need to consider the arrangement
of the image.
4.Players can try different arrangements of the puzzle pieces to find
the correct placement of each pieces.
5.The puzzle is considered complete when all pieces are correctly
assembled.
6. Clap your hands when you completely assemble the puzzle.

Objectives:
At the end of the lesson the learners are able to:
a.Describe the different reflection symmetry; and
b.Demonstrate a deep understanding of reflection as a
transformation that creates mirror images

Mechanics:
1.There are questions in each number.
2.You need to find the answer in the box.
3.Every correct answer corresponds to 3
points.
4.The team who will find the more words will
be declared the winner.

1.Is defined as a transformation
that creates a mirror image of a
geometric figure by flipping it
over a line.

2.Also known as reflection
symmetry.

3.Reflection involves flipping a
figure over a line.

4. Is a type of symmetry where a
figure is flipped over a line.

5.Is the reflection of a figure
across a line.

6. Is essential tools that reflect light to
create images, allowing us to see our
surroundings and ourselves.

7.Occur when a figure is
reflected more than once
across different lines of
reflection.

8. Is a fundamental concept in
mathematics and art that refers to a
balanced and harmonious
arrangement of parts.

9. Is fundamental elements in
mathematics and geometry.

10.Is fundamental elements in
geometry that define the form
and structure of objects in
space.

Reflection in mathematics is a type of rigid
geometrical transformation that maintains
the object's size and shape, unlike other
transformations such as dilation, which
changes the size of the shape, reflection
results in congruent images.

Figure 1
shows a tree and its reflection on the water. Mathematically, it
will be stated as the image of the tree is visible on the water and
the line of reflection in the imaginary line over the horizon.

Reflection in a Line
The line of reflection allows for the distinction of congruent images (preimage
and image). The line of reflection is a perpendicular bisector in response to the
congruent images. Hence, it divides a plane into two congruent or equal parts.
Figure 2
Diagram showing reflection across the Y-axis.
An illustration of a reflection math example in
the coordinate plane, it shows the following:

Is the preimage, meaning the original image before the
transformation.
Is the image (same letters but add dash), meaning the
mirror reflection after the transformation.
The y-axis, the line of reflection, as it divides the plane
into two congruent or equal parts.
Mathematically it can be stated that is the reflection of
over the y-axis.

Reflection in X-axis
In this section, the line of reflection is the x-axis. This means that the x-
axis is the perpendicular bisector of the preimage and image.
Figure 3 Diagram showing reflection across the X-axis
When the line of reflection is the x-axis the (x, y) transforms into (x,-y),
hence keeping x the same but flipping the y to a negative. The illustration
(figure 3) shows the following:

∆ABC, with coordinates, (7,4), (4,3), and (6,2) in the preimage flip to
∆ABC, with coordinates (7, -4), (4, -3), and (6,-2) in the image.
Reflection in a point
In geometry an object typically when having a reflection will have a
line of reflection, but there are some occasions on which a line is not
necessary to obtain a reflection. Such occasion is when an object is
constructed around a single point.

In figure 4 the illustration shows, that the reflection point is
labeled M. All other points have an exact opposite point on the
other side of M. Since the points are exactly the same, setting the
points together will provide a congruent object, same size, same
shape.

The bisector of the plane is known as the definition on the line of
reflection, and it is perpendicular to the preimage and image. A line
of reflection could be any line in a coordinate plane. To find the
reflection of an object, focus on the line of reflection:
1. When the line of reflection is the x-axis the (x, y) transforms into
(x, -y).
2. When the line of reflection is the y-axis the (x, y) transforms into
(-x, y).

A reflection of an object is the 'flip' of that object over a line, called the
line of reflection. In the following picture, the birds are reflected in the
water.
Their image is flipped over the line created by the edge of the water. Lines
of reflection do not have to be horizontal; they can also be vertical or
sloped in any direction.
The following image shows a vertical line of reflection:

The following image shows a vertical line of reflection:
The next image shows a figure reflected twice. You can see that the red preimage is reflected to
give the green image, and then, the green image is reflected again to give the second red image:

STEP 1: The vertices of the given polygon are A, B, C and D. From the graph, we
determine
A(4,-2), B(6,-4), C(10,0), and D(6,2).
STEP 2: Since we are reflecting the polygon over the line y=x, we obtain the
vertices of our reflected polygon by switching the x- and y-coordinates of each
point. This gives:
A(4,-3) A’(-2,4)
B(6,-4) B’(-4,6)
C(10,0) C’(0,10)
D(6,2) D’(2,6)

1.What is reflection in geometry?
A) A transformation that rotates a figure
around a point
B) A transformation that flips a figure over
a line
C) A transformation that stretches a figure
D) A transformation that compresses a
figure

2.Which of the following lines represents
a line of reflection?
A) y = 2x
B) x = -3
C) y = -x
D) x = 4

3.If a point P(3, 4) is reflected across the
line y = 2x, what are the coordinates of
the reflected point?
A) (4, 3)
B) (4, 6)
C) (2, 3)
D) (3, 2)

4.Which of the following shapes has
reflection symmetry?
A) Equilateral Triangle
B) Circle
C) Rectangle
D) Irregular Pentagon

5. Reflect the point A(2, 3) across the line y = -
x. What are the coordinates of the reflected
point?
A) (-3, 2)
B) (3, -2)
C) (-2, -3)
D) (2, 3)

6.What type of symmetry is exhibited by a figure
that remains unchanged after a reflection?
A)Rotational Symmetry
B)Translational Symmetry
C)Reflectional Symmetry
D)Point Symmetry

7.Reflect the triangle with vertices A(1, 2), B(3,
4), and C(5, 2) across the line y = 3. What are
the coordinates of the reflected triangle?
A) A'(1, 1), B'(3, 3), C'(5, 1)
B) A'(1, 4), B'(3, 6), C'(5, 4)
C) A'(1, 3), B'(3, 5), C'(5, 3)
D) A'(1, 5), B'(3, 7), C'(5, 5

8.Why is reflection important in modern
geometry?
A) It helps in stretching shapes
B) It aids in understanding symmetry
and transformations
C) It has no practical applications
D) It only works on regular polygons

9.In a reflectional symmetry, what is the
relationship between a figure and its
reflection?
A) They are identical
B) They are rotated by 90 degrees
C) They are translated vertically
D) They are compressed

10. Provide an example of a real-life
application where reflection is used in
design or architecture.
A) Bridges
B) Tunnels
C) Mirrored facades in buildings
D) Parks

Solve this.
Problem 1: Reflecting a Point Across a Line
Given a point P(3, 4) and a line of reflection y = x, reflect
the point P across the line of reflection.
Problem 2: Reflecting a Triangle Across a Horizontal Line
Given a triangle ABC with vertices A(2, 3), B(4, 5), and C(6,
3), reflect the triangle across the horizontal line y = 4.
Problem 3: Reflecting a Quadrilateral Across a Vertical Line
Given a quadrilateral PQRS with vertices P(1, 2), Q(3, 4),
R(3, 1), and S(1, -1), reflect the quadrilateral across the
vertical line x = 2.

PowerPoint presentation about modern geometry

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