Question

lesson 9.4 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.
complete the lesson reflection above by circling your current understanding of the learning goal.

1. observe the following quadrilaterals. they each have been labeled with a specific name. determine if the quadrilateral was given the correct name and explain your reasoning below each quadrilateral. if there is a more specific name, state it and explain your reasoning.

Explanation:

Analyze the first quadrilateral

Using the Quadrilateral Hierarchy knowledge point

• All four sides are equal to \(11.9\).
• Opposite angles are equal (\(110^\circ\) and \(70^\circ\)).
• Since all four sides are equal, this is a rhombus.
• "Rhombus" is more specific than "Parallelogram".

Analyze the second quadrilateral

Using the Properties of Squares knowledge point

• All four sides are equal to \(8.2\).
• All four angles are right angles (\(90^\circ\)).
• Since it has four equal sides and four right angles, it is a square.
• "Square" is more specific than "Rectangle".

Analyze the third quadrilateral

Using the Properties of Rectangles knowledge point

• Opposite sides are equal (\(11.2\) and \(9.6\)).
• All four angles are right angles (\(90^\circ\)).
• This meets the exact definition of a rectangle.
• "Rectangle" is the most specific name.

Analyze the fourth quadrilateral

Using the Rhombus Properties knowledge point

• All four sides are equal to \(13.2\).
• Opposite angles are equal (\(102^\circ\) and \(78^\circ\)).
• This meets the exact definition of a rhombus.
• "Rhombus" is the most specific name.

Answer:

Question 1

• Given Name: Parallelogram
• Correct or More Specific Name: Rhombus
• Reasoning: All four sides are equal (\(11.9\)), which makes it a rhombus. A rhombus is a more specific classification than a parallelogram.

Question 2

• Given Name: Rectangle
• Correct or More Specific Name: Square
• Reasoning: All four sides are equal (\(8.2\)) and all angles are \(90^\circ\). A quadrilateral with four congruent sides and four right angles is a square, which is more specific than a rectangle.

Question 3

• Given Name: Rectangle
• Correct or More Specific Name: Rectangle (Correct)
• Reasoning: The opposite sides are equal (\(11.2\) and \(9.6\)) and all angles are \(90^\circ\). Since adjacent sides are unequal, it cannot be classified as a square. Rectangle is the most specific name.

Question 4

• Given Name: Rhombus
• Correct or More Specific Name: Rhombus (Correct)
• Reasoning: All four sides are equal (\(13.2\)) and opposite angles are equal but not \(90^\circ\). This fits the definition of a rhombus, which is the most specific name.