Question

Which descriptions can describe more than one triangle? check all that apply

Answer 1

The descriptions which can describe more than one triangle is:

• angle measurements of 35°,35° and 110°.

• angle measurements of 40°,60° and 80°.

Explanation:

• The three given side lengths form a triangle if the sum of any 2 sides is greater than the length of the third side.

• Also, all the three given angle measure form a triangle if the sum of all the three angles is equal to 180 degree.

• We know that with the help of given side three lengths of a triangle a unique triangle is formed.

• and with the help of given three angle measures of a triangle more than one triangle is possible with distinct side length.

a)

Side lengths 6 ft, 8 ft and 10 ft.

First we check whether it form a triangle or not:

6+8=14>10

8+10=18>6

and

6+10=16>8

Yes, these side lengths form a triangle.

With the help of this only one unique triangle is possible.

b)

angle measurements of 35°,35° and 110°

First we check the sum of the angles:

35°+35°+110°=180°

Hence, more than one triangle is possible.

c)

angle measurements of 30°,40° and 50°

First we check the sum of these angles:

30°+40°+50°=120°≠180°

Hence, these angles measure do not form a triangle.

d)

angle measurements of 40°,60° and 80°

First we check the sum of these angles:

40°+60°+80°=180°.

Hence, more than one triangle is possible.

e)

side length of 4 cm, 6 cm and 9 cm.

First we check whether it form a triangle or not:

4+6=10>9

6+9=15>4

and

4+9=13>6

Hence, a unique triangle will be formed.

Answer 2

Angle measurements of 35°, 35°, and 110°

Angle measurements of 40°, 60°, and 80°

Explanation:

If you specify only the three angles, you can have an infinite number of similar triangles of different sizes.

A is wrong. There can be only one triangle in which all three side lengths are specified.

C is wrong. The angles do not add up to 180°.