Module 7. 3 – Triangle Inequalities. Today you will need your:. Notes

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Presentation transcript:

Module 7. 3 – Triangle Inequalities. Today you will need your:. Notes Module 7.3 – Triangle Inequalities Today you will need your: Notes Textbook

Triangle Inequalities – what makes a triangle? Picture a segment

Triangle Inequalities – what makes a triangle? Put a congruent segment right on top of the first segment.

Triangle Inequalities – what makes a triangle? Now split that segment in half and try to make a triangle.

Triangle Inequalities – what makes a triangle? Now split that segment in half and try to make a triangle.

Triangle Inequalities – what makes a triangle? Now split that segment in half and try to make a triangle.

Triangle Inequalities – what makes a triangle? You can’t make a triangle because the two sides won’t reach. The sum of the two red segments is equal to the length of the black segment. What MUST the sum of the red segments be in order to actually make a triangle?

Triangle Inequalities – what makes a triangle?

Triangle Inequalities – what makes a triangle? The sum of the lengths of the red segments must be GREATER than the length of the black segment!

Triangle Inequality theorem. The sum of any two side lengths of a triangle is greater than the third side length.

No: 5 + 3 < 9 Yes Yes No: 5 + 5 = 10 No: 7 + 13 = 20 Yes Triangle Inequality theorem. Can triangles with the following three side lengths actually exist. #1 10 13 20 #2 5 5 10 #3 4 3 2 #4 5 3 9 #5 6 6 #6 20 7 13 Yes No: 5 + 3 < 9 No: 5 + 5 = 10 Yes No: 7 + 13 = 20 Yes

Triangle Inequalities – what makes a triangle? Find the range of possible values for the missing side of a triangle. x 4 cm 10 cm

Triangle Inequalities – what makes a triangle? How small can the ‘x’ be? x > 10 - 4 x > 6 x 4 cm 10 cm

Triangle Inequalities – what makes a triangle? How large can the ‘x’ be? x < 10 + 4 x < 14 x 4 cm 10 cm

Triangle Inequalities – what makes a triangle? The possible value of ‘x’ must be between 6 and 14 centimeters. 6 < x < 14 x 4 cm 10 cm

Triangle Inequalities – what makes a triangle? Determine the range of values for ‘x’ in the following diagrams: 21 – 14 < x < 21 + 14 18 – 9 < x < 18 + 9 7 < x < 35 9 < x < 27

Relationships between side lengths and angle lengths in triangles Notice what happens to C as ∠1 is increased: 1 C

Relationships between side lengths and angle lengths in triangles Notice what happens to C as ∠1 is increased: 1 C

Relationships between side lengths and angle lengths in triangles Notice what happens to C as ∠1 is increased: 1 C

Relationships between side lengths and angle lengths in triangles Notice what happens to C as ∠1 is increased: 1 As ∠1 increases, side C increases. C

Relationships between side lengths and angle lengths in triangles The largest angle will always be across from the largest side. The largest angle will always be across from the largest side. The smallest angle will always be across from the smallest side. The middle angle will always be across from the middle side. 1 B The smallest angle will always be across from the smallest side. 2 A The middle angle will always be across from the middle side. C 3

Relationships between side lengths and angle lengths in triangles Order the sides/angles from smallest to greatest: ∠A < ∠B < ∠C CB < AB < AC

Classwork/Homework Page 348, #’s 1-10 Page 349, #’s 13-17