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# Determining if a Triangle is Possible. How many different acute triangles can you draw? How many...

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Determining if a Triangle is Possible
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Determining if a Triangle is

Possible

How many different acute triangles can you draw?

How many different right scalene triangles can you draw?

Recall that triangles can be classified according to their side lengths and the measure of their angles.

Sides:Scalene - no sides are congruentIsosceles - two sides are congruentEquilateral - all three sides are congruent

Angles:Acute - all three angles are acuteRight - contains one right angleObtuse - contains one obtuse angle

Example:

Determine if sides of length 5 cm, 8 cm and 12 cm can form a triangle?

Test the smallest 2 sides to see if the sum is greater:5 + 8 > 12 13 > 12

Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.

Example:

Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle?

Test the smallest 2 sides to see if the sum is greater:3 + 4 > 9 7 > 9

No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.

Try These:Determine if triangles can be formed with the following side lengths:

1. 4 cm, 7 cm, 10 cm 2. 24 mm, 20 mm, 30 mm

4 + 7 > 10 24 + 20 > 304 + 10 > 7 24 + 30 > 207 + 10 > 4 20 + 30 > 24 YES YES

3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in

7 + 9 = 16 9 + 13 < 247 + 16 > 9 9 + 24 > 1316 + 9 > 7 13 + 24 > 9NO NO

1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work!

A Yes

B No

1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work!

A Yes

B No

5 + 14 < 19? 19 = 19

2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work!

A Yes

B No

2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work!

A Yes

B No

6 + 9 > 14 ? 15 > 14

3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work!

A Yes

B No

3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work!

A Yes

B No

5 + 13 > 21 ? 18 < 21

4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work!

A Yes

B No

4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work!

A Yes

B No

3 + 8 > 15 ? 11 < 15

5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work!

A Yes

B No

5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work!

A Yes

B No

5 + 5 > 9? 10 > 9

Example:

Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft.

Example:

Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft.

Side 1 = 12 ft and Side 2 = 16 ft. Let x = the 3rd Side

Example:

Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft.

Side 1 = 12 ft and Side 2 = 16 ft, let x = the 3rd Side

What if the 3rd side is the LARGEST number?: 12 + 16 > x 28 > x

Example:

Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft.

Side 1 = 12 ft and Side 2 = 16 ft, let x = the 3rd Side

What if the 3rd side is the LARGEST number?: 12 + 16 > x 28 > x

What if the 3rd side is the SMALLEST number?:12 + x > 16 x > 4

Example:

Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft.

Side 1 = 12 ft and Side 2 = 16 ft, let x = the 3rd Side

What if the 3rd side is the LARGEST number?: 12 + 16 > x 28 > x

What if the 3rd side is the SMALLEST number?:12 + x > 16 x > 4

The 3rd side must be greater than 4 ft and less than 28 ft.Write this as the compound inequality: 4 < x < 28

Example:

Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm.

Example:

Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm.

Side 1 = 9 cm and Side 2 = 15 cm. Let x = the Third side

Example:

Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm.

Side 1 = 9 cm and Side 2 = 15 cm. Let x = the Third side

If the third side is the LARGEST side: 9 + 15 > x24 cm > x

Example:

Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm.

Side 1 = 9 cm and Side 2 = 15 cm. Let x = the Third side

If the third side is the LARGEST side: 9 + 15 > x24 cm > x

If the third side is the SMALLEST side:9 + x > 15 x > 6 cm

Example:

Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm.

Side 1 = 9 cm and Side 2 = 15 cm. Let x = the Third side

If the third side is the LARGEST side: 9 + 15 > x24 cm > x

If the third side is the SMALLEST side:9 + x > 15 x > 6 cm

The 3rd side must be greater than 6 cm and less than 24 cm.Write this as the compound inequality: 6 cm < x < 24 cm

Try These:Predict the length of the third side of a triangle whose known sides are lengths:

1. 13 mm & 20 mm 2. 7 in & 19 in

13 + 20 > Side 3 7 + 19 > Side 3 33 > Side 3 26 > Side 3

13 + Side 3 > 20 7 + Side 3 > 19 Side 3 > 7 Side 3 > 12

7 < side 3 < 33 12 < side 3 < 26

Try These:Predict the length of the third side of a triangle whose known sides are lengths:

3. 4 ft, 11 ft 4. 23 cm, 34 cm

4 + 11 > Side 3 23 + 34 > Side 315 > Side 3 57 > Side 3

4 + Side 3 > 11 23 + Side 3 > 34 Side 3 > 7 Side 3 > 11

7 < side 3 < 15 11 < side 3 < 57

8 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.

9 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.

10 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.

11 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.

12 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.

13 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.

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