Question

Meg described four triangles as shown below:

Triangle P: All sides have length 7 cm.
Triangle Q: Two angles measure 55°.
Triangle R: Two sides have length 8 cm, and the included angle measures 60°.
Triangle S: Base has length 8 cm, and base angles measure 55°.

Which triangle is not a unique triangle? PLEASE HELP

Answer 1

The triangle which is not a unique triangle is:

Triangle Q.

Explanation:

• As we know that with the help of given three side lengths a unique triangle is constructed.

Hence, Triangle P will be unique.

• Also, with the help of the given three angle measure infinite number of triangles could be constructed as the side lengths may be different.'

Hence, Triangle Q is not unique.

( Since we are given two angles and the measure of the third angle could be known with the help of property that:

Sum of all the angles of a triangle is 180° )

• Also, with the help of a given two side lengths and a included angle measure a unique triangle is constructed.

( Since, we make a line segment of given length and then keep the compass at one of end point and make a 60 degree angle and cut that side into length 8 cm and finally join the other end point and the constructed line to get a triangle)

Hence, Triangle R is also unique.

• Similarly Triangle S will also be unique by construction.

( First draw a line segment of length 8 cm and at both the ends of the line make a 50 degree angle and extend the line over the arc of the angle and see where two lines intersects.

By such a way we obtain a unique triangle)