Look no further for fun ways to involve learners with the theorem of Pythagoras while introducing the topic of Euclidean Geometry.

1. Grade 10 Lesson Plan
Recap of the Pythagorean Theorem and
introduction to Euclidean Geometry
Based
On

2. MATHEMATICS GRADE 10: THE THEOREM OF PYTHAGORAS AND
EUCLIDEAN GEOMETRY
SUB TOPIC: SOLVING PROBLEMS USING THE THEOREM OF
PYTHAGORAS AND ITS LINK TO EUCLIDEAN GEOMETRY.
DURATION: 1 WEEK: LESSON DISCUSSION AND GAME TO TAKE 2
PERIODS OR 80MIN. INTRODUCTION TO EUCLIDEAN
GEOMETRY AND WORKSHEET TO BE DONE OVER 2 PERIODS
OR 80MIN
AT THE END OF THIS LESSON LEARNER’S SHOULD BE ABLE TO:
 Students should state the Pythagorean theorem
 Prior knowledge of the Pythagorean equation and how to use it
 They should know the various types of triangles as well as their
properties
 The different types of angles and how to measure an angle
 They should be able to do simple arithmetic without the aid of a
calculator
 Must manipulate the question to find the answer or try new
ways off solving the problem, they should also be creative and
come up with their own ways off solving or understanding the
work.
LESSON DISCUSSION AND ACTIVITIES
The following to be written in their books
BACKGROUND
The Pythagorean Theorem was one of the earliest theorems
known to ancient civilizations. This famous theorem is named for
the Greek mathematician and philosopher, Pythagoras.
The Pythagorean Theorem is a statement about triangles
containing a right angle. The Pythagorean Theorem states that:
"The area of the square built upon the hypotenuse of a right
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3. triangle is equal to the sum of the areas of the squares upon the
remaining sides."
This Theorem can be proved by the following diagram:
If a triangle has a right-angle (90o
) and you made a square on each
of the three sides (a, b & c), then the biggest square has the exact
same area as the other two squares put together:
Hence:
Area of square A = a2
Area of square B = b2
Area of square C = c2
Therefore the Pythagoras theorem can be written in one short
equation i.e. a2
+ b2
= c2
Now that the learners have recapped the theorem, it’s time to solve problems with the
aid of the theorem. Complete game one and two (not in books)
FOR TEACHERS REFFERENCE
GAME ONE: TEACHER INSTRUCTIONS ON PYTHAGORAS
Introduction
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4. They say his fast, silent, dangerous, deadly! And untraceable!! He has
become famous. He apparently started hacking into various companies,
finding track records of young attractive woman and kidnapping them…
one from of our very school system. Only after a child went missing and
was killed did we pick up traces of this idea. More students came forth
with their stories, but this lead us no closer to finding this killer. This
means he is still on the loose. The CIA approached us to solve their
mystery…could it be you? The one next to you?? Me??? (I see a guilty
conscience) …I urge you to help by looking around you for clues
(Clues placed under desks and chairs or on the walls). Clues are dependent on
each class as the alphabets numerical value changes. Note to make the lesson
fun: use clues that lead to a student well known .Reward the student who gave
the correct answer
Thereafter when the class settles, for interest sake we can relate examples
to real life situations (depending on time)
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Clue 1
Clue 2
Clue 4
Clue 5 Clue 6
Clue 3
4

5. GAME TWO: TEACHER INSTRUCTIONS ON LINES ANGLES AND
TRIANGLES.
Introduction
We are working on geometry right now. More specifically, last year we did
some activities with lines, rays, and line segments. This is important for
the upcoming lesson.
I thought I would share how to reinforce the definitions of each. As we go
over each part, we will build them, using; toothpicks, candy corns, and
marshmallows. The marshmallows were the points. The candy corns
showed how the straight path continued in a direction, and of course, the
toothpick was the straight path.
Thus creating a group activity for all students. Allowing them to see lines, angles
and triangles in a different way.
Follow the learner instructions.
And assist each group as they go along with the activity
*To draw on the overhead projector
All drawings will be drawn on the black board, transparencies for
the overhead projector or on the smart board. Whichever is
available at the school.
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6. HANDOUTS
GAME ONE: PYTHAGORAS
Instructions: Learner Activity
• There are clues placed in and around our classroom
• Work in groups of five, one person from each group will go search for a
clue
• Once you find a clue, you return to the class and your group
• Immediately start to solve the mathematical equation for the unknown
side.
• Thereafter relate the number to alphabet of that numerical value as per
clue.
For example:
• Once you find the alphabet come to the front and peg the letter on the
line
• Thereafter the class as a whole will be able to figure out the name of the
killer
This process should take up roughly 25minutes
Thereafter for interest sake we can relate examples to real life situations
• Example : use a ruler to divide a class into two
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Answer for each unknown side + equation = an alphabet
Clue 4: first: a2
+ b2
= c2
(3)2
+ (4)2
= c2
5 = c
Then: C + 1 = alphabet
5 + 1= 6th
alphabet
F
C + 1 = alphabet

7. • Another example: a simple golf course
• How would they get the ball in the hole under par
• Draw a right angled triangle
• Thus calculate the single distance they would need to hit a hole in one.
This activity can take up to 25 minutes as well
GAME TWO: LINES, ANGLES AND TRIANGLES
I thought I would share how to reinforce the definitions of lines, angles and
triangles. As we go over each part, we will build them, using; toothpicks, candy
corns, and marshmallows. The marshmallows were the points. The candy corns
showed how the straight path continued in a direction, and of course, the
toothpick was the straight path.
Learner Activity:
Each group is given: three tooth picks, six marshmallows and two candy
corns
• Each group must use the given objects to create the terms: points,
segments and straight path by building them.
• Then create the various types of triangles (e.g. Equilateral, right
angled…) learned from prior lessons with the given objects.
(The first group to name a triangle un-said receives free sweets for the
group.)
I WILL DRAW THE TRIANGLE ON THE OVERHEAD SO THE REST OF
THE CLASS UNDERSTANDS.
• Name and create different angles as well as parallel and
perpendicular lines
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8. Looking at the diagram below:
On a piece of paper as a group, identify any theorems, triangles and lines which
are visible within the circle. Hint: you can draw in lines to form other triangles
DON’T FORGET TO WRITE ALL GROUP MEMBERS NAMES ON THE
PAPER.
TO HAND IN AT THE END OF THE LESSON.
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