Determining if a Triangle is Possible

Return to table of contents

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

There is another property that applies to triangles:

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

What does this mean?

If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side.

If that is not true, then it is not possible to construct a triangle with the given side lengths.

Example:

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

Test all three pairs to see if the sum is greater:5 + 8 > 12 5 + 12 > 8 8 + 12 > 5 13 > 12 17 > 8 20 > 5

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 all three pairs to see if the sum is greater:3 + 4 > 9 3 + 9 > 4 4 + 9 > 3 7 > 9 12 > 4 13 > 3

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

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

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

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

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

6 A triangle could have which of the following sets of angles?

ABCD

7 A triangle could have which of the following sets of angles?

ABCD

Example:

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

Side 1 = 12 ftSide 2 = 16 ft

The 3rd side must be less than: 12 + 16 > 3rd side 28 ft > 3rd side

The 3rd side must be greater than:12 + 3rd side > 16 3rd side > 4

The 3rd side must be greater than 4 ft and less than 28 ft.

Example:

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

Side 1 = 9 cmSide 2 = 15 cm

The 3rd side must be less than: 9 + 15 > 3rd side24 cm > 3rd side

The 3rd side must be greater than:9 + 3rd side > 15 3rd side > 6

The 3rd side must be greater than 6 cm and less than 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.