Drawing geometric shapes from conditions Knowledge-Based Practice

Questions

1. 1.

   Given only the length of a single diagonal, which of the following quadrilaterals is uniquely determined?

   • A) A square
   • B) A rectangle
   • C) A rhombus
   • D) A parallelogram
2. 2.

   Which of the following sets of conditions is sufficient to construct a unique parallelogram $ABCD$?

   • A) The lengths of all four sides
   • B) The lengths of two adjacent sides and the measure of their included angle
   • C) The lengths of the two diagonals
   • D) The measures of all four interior angles
3. 3.

   Which of the following sets of given conditions makes it impossible to construct any triangle $\triangle ABC$?

   • A) $AB = 5$ cm, $BC = 7$ cm, and $AC = 9$ cm
   • B) $AB = 3$ cm, $BC = 4$ cm, and $AC = 8$ cm
   • C) $\angle A = 55^\circ$, $\angle B = 65^\circ$, and $AB = 6$ cm
   • D) $AB = 5$ cm, $BC = 8$ cm, and $\angle B = 60^\circ$
4. 4.

   Which of the following sets of given conditions results in the construction of more than one non-congruent triangle $\triangle ABC$?

   • A) $\angle A = 45^\circ$, $\angle B = 65^\circ$, and $AB = 6\text{ cm}$
   • B) $AB = 5\text{ cm}$, $AC = 8\text{ cm}$, and $\angle A = 60^\circ$
   • C) $\angle A = 30^\circ$, $AC = 10\text{ cm}$, and $BC = 7\text{ cm}$
   • D) $AB = 3\text{ cm}$, $BC = 4\text{ cm}$, and $AC = 9\text{ cm}$
5. 5.

   Which of the following sets of conditions determines exactly one unique triangle $\triangle ABC$?

   • A) $m(\angle A) = 50^\circ$, $m(\angle B) = 60^\circ$, and $m(\angle C) = 70^\circ$
   • B) $AB = 7\text{ cm}$, $BC = 10\text{ cm}$, and $m(\angle B) = 45^\circ$
   • C) $AB = 4\text{ cm}$, $BC = 5\text{ cm}$, and $AC = 11\text{ cm}$
   • D) $AB = 8\text{ cm}$, $BC = 5\text{ cm}$, and $m(\angle A) = 30^\circ$

Answers and step-by-step solutions appear after you finish the test.