Question

Zeda described four triangles as shown below: Triangle P: Two angles measure 50°. Triangle Q: All sides have length 13 cm. Triangle R: Two sides have length 3 cm, and the included angle measures 60°. Triangle S: Base has length 5 cm, and base angles measure 30°. Which triangle is not a unique triangle? Triangle P Triangle Q Triangle R Triangle S

Answer 1

I think it is P. Because the rest are isosceles.

Answer 2

Answer: Triangle P

Explanation:

Given:

• Triangle P: Two angles measure 50°.

If any triangle have same measurement it must be similar to triangle P by AA similarity criteria but not congruent.

Hence it is not unique.

• Triangle Q: All sides have length 13 cm.

Since all sides have same length, thus it must be an equilateral triangle with all angles 60 °.

If any triangle have same sides it must be congruent to this by SSS congruence rule.

Hence, it is unique.

• Triangle R: Two sides have length 3 cm, and the included angle measures 60°.

If any triangle exists with same measure as triangle R then it must be congruent to triangle R by SAS congruence criteria.

Hence, it is unique.

• Triangle S: Base has length 5 cm, and base angles measure 30°.

If any triangle exists with same measure as triangle R then it must be congruent to triangle R by ASA congruence criteria.

Hence, it is unique.