Quiz 29

Which of the following conditions form a unique triangle?

• a 90° angle and two 45° angles

• a 3 cm side between a 90° and a 60° angle

• a 3 cm side, a 4 cm side, and an 8 cm side

• a 3 cm side between a 120° and a 100° angle

1. Which conditions form a unique quadrilateral? Choose all the correct answers.

• a quadrilateral with four right angles and with side lengths that are
  each 4 ft long

• a rhombus with a side length of 4 cm

• a rectangle with side lengths of 10 cm and 15 cm

• a quadrilateral with side lengths of 5 m, 7 m, 8 m, and 2 m

• a parallelogram with a 50° angle and a 12-in. side

Declan and Jen are working on a school project. They each need to cut out and decorate a triangle with sides that are 8 cm and 10 cm long, with a 100° angle.

Do these conditions require that the triangles Declan and Jen draw be the same?

Explain your reasoning. Use a drawing.

Megan draws a parallelogram with one right angle and four sides that are each 3 cm long. Julio draws a square with sides that are 3 cm long. Linnea says they must be the same quadrilateral. Is Linnea correct? Explain your reasoning.

What does each set of conditions describe? Decide if each set of conditions forms one triangle, more than one triangle, or no triangle.

Groups:

(a) One Triangle

,

(b) More Than One Triangle

,

(c) No Triangle

• Side lengths

• angle measures 30°, 60°, and 90°

• one right angle and one

  100° angle

• two 3-in. sides and one 7-in. side

• angle measures 90° and 37° and

  a 9-yd side

• all sides of length 8 ft