Triangles

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Philosophy of Mathematics

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Additional Information

Useful websites

1. All about triangles

This is a reference website for types and classification off triangles

1. http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm

A good website for quick reference of all theorems in geometry. Suitable for both students and teachers.

1. Click here for notes on types of triangles.
2. Click here for notes on types of triangles.

Teaching Outlines

Concept #1 A triangle and its properties

Learning objectives

1. A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments.
2. It is the polygon with the least number of sides.
3. A triangle can be defined as a polygon which has 3 sides, 3 angles and 3 vertices.
4. The sum of any two sides is always greater than the third side.
5. The angle opposite to longest side is the largest.
6. The sum of all 3 angles in any triangle is always 180 degrees which is called the angle sum property of a triangle.

Notes for teachers

[These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.]

1. A triangle PQR consists of all the points on the line segment PQ,QR and RP. The three line segments, PQ, QR and RP that form

the triangle PQ, are called the sides of the triangle PQR.

1. A triangle has three angles. In figure, the three angles are ∠PQR ∠QRP and ∠RPQ
2. A triangle has six parts, namely, three sides,PQ QRand RP.Three angles ∠PQR ∠QRP and ∠RPQ. These are also known as the elements of a triangle.
3. The point of intersection of the sides of a triangle is known as its vertex. In figure, the three vertices are P, Q and R. In a triangle, an angle is formed at the vertex. Since it has three vertices, so three angles are formed. The word triangle =tri + angle ‘tri’ means three. So, triangle means closed figure of straight lines having three angles.

Activity No # 1 Make your triangle

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• Estimated Time - 40 minutes
• Materials/ Resources needed; Paper, pencil, and scale.
• Prerequisites/Instructions, if any:

1. The students should know points and line segments.

• Multimedia resources
• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity):

1. Mark three non-collinear point P, Q and R on a paper.
2. Join these points in all possible ways. The segments are PQ, QR and RP.
3. A simple close curve formed by these three segments is called a triangle. It is named in one of the following ways.
4. Triangle PQR or Triangle PRQ or Triangle QRP or Triangle RPQ or Triangle RQP .

PQR

• Developmental Questions (What discussion questions):

1. What are plane figures ?
2. What is a polygon ?
3. How many points are needed to make a traingle ?

• Evaluation (Questions for assessment of the child):

1. What are the intersecting points of a triangle called ?
2. Can you draw a triangle with collinear points.

• Question Corner

1. Name the elements of a triangle.

Activity No # 2 - Types of triangles - Identifying and naming

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Part 1

• Estimated time - 20 minutes
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources

• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)

Identify and name the triangles in the above figure.

• Evaluation

1. Is it possible to construct a triangle with 3 collinear points?
2. Is it possible to construct a triangle whose sides are 3cm, 4cm and 9cm. Why?.

Part 2

• Estimated time - 20 minutes
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources

Look at the following images below

• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)

Identify and name the triangles in the above figure.

• Evaluation

1. Can a scalene triangle also be a right-angled triangle ? If yes can you draw one ?

Concept #2 - Properties and Theorems: Thales Theorem

Notes for teachers

1. The GeoGebra file below verifies the Thales theorem
   

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activity No #

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• Estimated Time
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)
• Developmental Questions (What discussion questions)
• Evaluation (Questions for assessment of the child)
• Question Corner

Activity No #

Click to Comment

• Estimated Time
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)
• Developmental Questions (What discussion questions)
• Evaluation (Questions for assessment of the child)
• Question Corner

Concept #3 - Properties and Theorems: Pythagoras Theorem

Notes for teachers

Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 BC and 500 BC. Pythagoras' Theorem states that:

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is:

Pythagoras' Theorem in Three Dimensions A three-dimensional object can be described by three measurements - length, width and height. We can use Pythagoras' Theorem to find the length of the longest straw that will fit inside the box or cylinder.

Activity No #

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• Estimated Time
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)
• Developmental Questions (What discussion questions)
• Evaluation (Questions for assessment of the child)
• Question Corner

Activity No #

Click to Comment

• Estimated Time
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ Geogebra Applets
• Process (How to do the activity)
• Developmental Questions (What discussion questions)
• Evaluation (Questions for assessment of the child)
• Question Corner

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