Kites and Squares

Properties of Kites

December 10, 2020

Multiple Choice

Do Now:

Use the distance and slope formulas to prove that the following parallelogram is a square.

A(2,6) B(7,6) C(7,1) D(2,1)

What’s the distance? What are the slopes?

• Distance: $$\sqrt{50}$$
  Slopes: $$1$$ and $$-1$$

• Distance: $$25$$
  Slopes: $$-\frac{1}{2}$$ and $$2$$

• Distance: $$\sqrt{10}$$
  Slopes: $$\frac{4}{5}$$ and $$-\frac{5}{4}$$

• Objective:  I can use properties of kites to solve mathematical problems.

  
  

• Essential Question: How can I show that a quadrilateral is a kite? What classifies a kite?

  
  

Agenda

• Do Now

• Recap

• Exploration

• Notes + Practice

• Asynchronous

Exploration

In today’s folder, use the applet in order to construct a kite.

What do you notice about the kite’s side and angles? (You can use the sample images).

Let us know in the chat.

Properties of Kites

If a quadrilateral is a kite, then its diagonals are perpendicular.

AC  $\perp$  BD

Notice*

Kites have exactly two pairs of consecutive congruent sides.

AB   $\cong$  AD

BC   $\cong$  CD

Properties of Kites

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

 $\angle$  B  $\cong$   $\angle$  D

Multiple Choice

If a quadrilateral is a kite, then its _________ are perpendicular.

• Diagonals

• Consecutive Sides

• Angles

Multiple Choice

If a quadrilateral is a kite, then it has exactly one pair of congruent opposite __________

• Diagonals

• Sides

• Angles

Multiple Choice

A kite is a quadrilateral with exactly two pairs of consecutive congruent _________.

• Diagonals

• Sides

• Angles

Fill in the Blanks

Use the figure to determine

$m\angle D$  

Fill in the Blanks

Use the figure to determine the length of AB.

Fill in the Blanks

Use the figure to determine the length of CD.

Whiteboard Example

Desmos Practice: 10-15 minutes

Class Codes:

M8UDQJ (A3)

N57C9G (A4)

Open Ended

Closure:

What are some differences or similarities between a kite and rhombus?

Poll

After exploring kites, working on examples, and working independently, I feel confident using properties of kites to find missing angle and side measurements.