Exploring Kites: Properties and Theorems

Objective:

Students will be able to identify the properties of kites and apply the Kite Diagonals Theorem to solve problems involving kites.

Assessment:

Students will complete a worksheet where they have to identify the properties of different kites and prove the Kite Diagonals Theorem by solving problems.

Key Points:

• Definition of a Kite: A kite is a quadrilateral with two distinct sets of adjacent congruent sides. If a kite is concave, it is called a dart.

• Properties of Kites:

  • The non-vertex angles of a kite are congruent.

  • The diagonal through the vertex angles is the angle bisector for both angles.

• Kite Diagonals Theorem: The diagonals of a kite are perpendicular.

• Additional Facts about Kites:

  • Congruent Angles: The non-vertex angles of a kite are congruent.

  • Angle Bisector: The diagonal through the vertex angles is the angle bisector for both angles.

  • Perpendicular Diagonals: The Kite Diagonals Theorem states that the diagonals of a kite are perpendicular.

Opening:

• Show students various images of kites and ask them what they notice about the shapes

• Discuss with students what they know about kites and how they think the diagonals of a kite are related

Introduction to New Material:

• Define a kite as a quadrilateral with two distinct sets of adjacent congruent sides

• Explain the key properties of kites and introduce the Kite Diagonals Theorem

• Anticipated misconception: students may confuse kites with other quadrilaterals like rhombuses or squares

Guided Practice:

• Provide examples of kites and guide students through identifying their properties

• Scaffold questioning from identifying congruent angles to applying the Kite Diagonals Theorem

• Monitor student performance by circulating the room and providing feedback as needed

Independent Practice:

• Assign a worksheet where students have to identify the properties of various kites and prove the Kite Diagonals Theorem through calculations

• Expect students to work independently and ask for help if needed

• Provide extension problems for students who grasp the material quickly

Closing:

• Have students share one new thing they learned about kites today

• Summarize the key properties of kites and the Kite Diagonals Theorem

Extension Activity:

• Challenge students to create their own kites using paper and other materials, ensuring they adhere to the properties discussed in class

Homework:

• Ask students to find real-life examples of objects that resemble kites and identify the properties that make them kites

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.D.13.A: Construct an inscribed square with one side on the circle and find the length of the side using the Pythagorean Theorem

• CCSS.MATH.CONTENT.HSG.CO.D.13.B: Explain and use the relationship between the sine and cosine of complementary angles