Question

Linda described four triangles as shown below:

Triangle A: All sides have length 7 cm.

Triangle B: All angles measure 60°.

Triangle C: Two sides have length 8 cm, and the included angle measures 60°.

Triangle D: Base has length 8 cm, and base angles measure 55°.

Which triangle is not a unique triangle?

Triangle A
Triangle B
Triangle C
Triangle D

Answer 1

@Nnesha

Answer 2

D

Answer 3

for sides 3rd side should be bigger than the sum of other 2 sides
\[\rm a+b >c\]\[\rm b+c > a\]\[\rm a+c >b\]
all triangles add up to 180 degree

Answer 4

We can prove two triangles congruent using ASA, SAS, SSS, etc. by finding the necessary pairs of congruent corresponding parts.

That means that, for example, if the description of the triangle has three given side lengths, then you have a unique triangle. That is how SSS works for proving triangles congruent.

Let's look at the 4 triangles described above.

Triangle A: All sides have length 7 cm.
With all side lengths given, you could use SSS to prove two triangles congruent, so choice A. definitely describes a unique triangle.

Triangle B: All angles measure 60°.
We are only told the measures of the three angles. That reminds us of AAA, which is really just AA which can be used for similarity but not for congruence. There is an infinite number of triangles with all 3 angles measures of 60 degrees.

Triangle C: Two sides have length 8 cm, and the included angle measures 60°.
Since you are given two side lengths and the measure of the included angle, this is a case of SAS. Since SAS works for proving triangles congruent, this is a description of a unique triangle.

Triangle D: Base has length 8 cm, and base angles measure 55°.
The base is one side. The base angles are on both sides of the given side, so this reminds us of ASA. Since ASA can be used for triangle congruence, then it must be describing a unique triangle.