Drawing geometric shapes from conditions Knowledge-Based Download PDF

Questions

1. 1.

   A student is asked to construct a triangle with two side lengths of 8 cm and 5 cm, and a non-included angle of 30° opposite the 5 cm side. How many non-congruent triangles can be drawn satisfying these conditions?

   • A) Exactly 2
   • B) Exactly 1
   • C) Infinitely many
   • D) None
2. 2.

   A student is asked to construct a triangle with interior angles measuring $35^\circ$, $55^\circ$, and $90^\circ$. How many non-congruent triangles can be drawn satisfying these conditions?

   • A) Zero triangles, because side lengths are required to form any triangle.
   • B) Exactly one unique triangle, because all three interior angles are fixed.
   • C) Exactly two non-congruent triangles, because the triangle can be reflected across an axis.
   • D) Infinitely many non-congruent triangles, because the side lengths can be scaled freely while preserving the angle measures.
3. 3.

   A student is asked to draw a quadrilateral with side lengths of 4 cm, 5 cm, 7 cm, and 9 cm given in that specific order. Which statement correctly describes the shapes that can be constructed under these conditions?

   • A) No quadrilateral can be drawn because four side lengths alone cannot satisfy the polygon inequality.
   • B) Exactly one unique quadrilateral can be drawn because specifying all four side lengths in order fixes the shape.
   • C) Infinitely many non-congruent quadrilaterals can be drawn because the interior angles can vary without changing the side lengths.
   • D) Exactly two non-congruent quadrilaterals can be drawn because the sides can only form one convex and one concave shape.
4. 4.

   A student is asked to draw a triangle with side lengths of 4 cm, 7 cm, and 12 cm. How many distinct triangles can be drawn under these conditions?

   • A) Exactly one unique triangle
   • B) Exactly two non-congruent triangles
   • C) Infinitely many non-congruent triangles
   • D) No triangle can be drawn
5. 5.

   Which of the following sets of conditions guarantees that exactly one unique triangle can be drawn?

   • A) Three interior angles measuring $35^\circ$, $65^\circ$, and $80^\circ$
   • B) Three side lengths measuring $4\text{ cm}$, $5\text{ cm}$, and $10\text{ cm}$
   • C) Two side lengths measuring $7\text{ cm}$ and $11\text{ cm}$ with no angle measures given
   • D) Two side lengths measuring $6\text{ cm}$ and $9\text{ cm}$ with an included angle measuring $50^\circ$