Triangle Inequalities by: Thess C. Reluba

Guess the Magic Word !

Read the question in Column A and click the correct answer in column B Read the question in Column A and click the correct answer in column B. Each answer corresponds to a letter or a code. Place them in the decoder to form the MAGIC WORD.

Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T O 11 10 7 2 9 5 6 1 3 4 8 B

Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A A S S T T O 11 10 7 2 9 5 6 1 3 4 8 B

Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T P T O 11 10 7 2 9 5 6 1 3 4 8 B

Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T P T I O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T P T I O O 11 10 7 2 9 5 6 1 3 4 8 B Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T P T I O O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T P R T I O O 11 10 7 2 9 5 6 1 3 4 8 B Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T P R T I O O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T O P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T O P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T O P R A T I O N O 11 10 7 2 9 5 6 1 3 4 8 Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T O P R A T I O N O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T O P E R A T I O N O Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T O P E R A T I O N O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T O O P E R A T I O N O Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T O O P E R A T I O N O 11 10 7 2 9 5 6 1 3 4 8 B

E O N I O C S P L O R A S T C O O P E R A T I O N O Column A Column B 1. A polygon with the least number altitude of sides bisector 2. A segment drawn from any vertex of the triangle to the midpoint of the opposite side complementary 3. The longest side in a right triangle hypotenuse 4. The sum of the interior angles of any triangle incenter 5. A triangle with one right angle isosceles triangle 6. It is a triangle with no equal sides legs 7. The point of concurrency of the bisectors median of the triangle orthocenter 8. The relation of the acute angles of the right triangle perpendicular The height of the triangle right triangle 10. The relation of the legs of the right triangle scalene triangle 11. A triangle with 2 equal sides supplementary Decoder: triangle 180° 360° E O N I O C S P L O R A S T C O O P E R A T I O N O 11 10 7 2 9 5 6 1 3 4 8 B

COOPERATION

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ACTIVITY # 1

Determine if the given combinations/triples can be formed into a triangle by joining the sticks at their endpoints.

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

Can you form a triangle with the ff. triples? Yes or No 2 , 2 , 3 Yes 2 , 3 , 4 5 , 4 , 3 3 , 4 , 7 No 5 , 5 , 5 7 , 5 , 6 6 , 4 , 2 7 , 2 , 4 3 , 5 , 7 2 , 3 , 6

If you have 2 sticks with lengths 5 cm and 8 cm, what are the possible integral values for the length of the 3rd side?

ACTIVITY # 2

Find the range of integral values for the length of the 3rd side and the number of triangles that can be formed

3 and 4 8 and 16 13 and 7 40 and 21 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 8 and 16 13 and 7 40 and 21

3 and 4 1 < 3rd < 7 8 and 16 13 and 7 40 and 21 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 8 and 16 13 and 7 40 and 21

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 13 and 7 40 and 21 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 13 and 7 40 and 21

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 13 and 7 40 and 21

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 15 triangles 13 and 7 40 and 21

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 15 triangles 13 and 7 6 < 3rd < 20 40 and 21

3 and 4 1 < 3rd < 7 6 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 6 triangles 8 and 16 8 < 3rd < 24 16 triangles 13 and 7 6 < 3rd < 20 13 triangles 40 and 21

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 15 triangles 13 and 7 6 < 3rd < 20 13 triangles 40 and 21 19 < 3rd < 61

3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 Given Range of possible length of the 3rd side # of triangles that can be formed 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24 15 triangles 13 and 7 6 < 3rd < 20 13 triangles 40 and 21 19 < 3rd < 61 41 triangles

The sum of any two sides must be greater than the third side. Generalization : The sum of any two sides must be greater than the third side.

The sum of any two sides must be greater than the third side. Generalization : The sum of any two sides must be greater than the third side. The length of third side must be greater than the difference but less than the sum of two sides.

Let’s check how well you know.

Two sides of a triangle measures 23 m and 7 m. Tell whether or not ( yes or no ) each of the following can be measurement for the 3rd side. a. 24 m b. 9 m c. 29 m d. 45 m e. 37 m

2. If a triangle has 2 sides measuring 9 units and 7 units, then the measure of the 3rd side is longer than ___ units and shorter than ___ units.

2. If a triangle has 2 sides measuring 9 units and 7 units, then the measure of the 3rd side is longer than ___ units and shorter than ___ units. 3. What is the range of possible integral values for the length of the third side if the lengths of two sides of a triangle are 6 and 12 ?

2. If a triangle has 2 sides measuring 9 units and 7 units, then the measure of the 3rd side is longer than ___ units and shorter than ___ units. 3. What is the range of possible integral values for the length of the third side if the lengths of two sides of a triangle are 6 and 12 ? 4. How many triangles with integral length can you form if the length of two sides are 15 and 10 ?

Time for home activity

Find the range of values of the diagonals AC and BD of the quadrilateral below. 2. Find the range of values for the legs of an isosceles triangle whose length base… a. 5 cm b. 11 m c. 7 cm