Lesson #14 - Kites

Initial posting - July, 2011 as Lesson 11
Revision date - Fall 2017

Purpose: This lesson introduces kites and should be a review of what you have learned about the Pythagorean Theorem. Knowledge of the sine function is necessary to complete Example 2.
Essential Question: Given a convex kite with a few measurements provided, can you use the Pythagorean Theorem and the sine function to calculate the missing angle measures and side lengths? Can you use Logo to test your calculations and code? Can you use these calculations to make generalizations about Kites?

A Section of the Lesson Follows

A kite is a quadrilateral with two distinct pairs of congruent adjacent sides. A kite can be either convex or concave. The diagonals of a kite intersect at a right angle. Note that the diagonals decompose the convex kite into two pairs of congruent right triangles. In Figure 14.1, triangles QAP and QAR are congruent. Triangles SAP and SAR are congruent. Two triangles are congruent if the corresponding angles and corresponding segments are congruent (i.e. segment AP is congruent to segment AR; angles QAP and QAR are congruent). You will use this relationship as you write the Logo code for a kite.
Example 1: Kite PQRSFind all of the unknown side and angle measures for the kite in Figure 14.1. Write and test the Logo Code starting at point P. The solution can be found at the end of this lesson.
*Example 2: Kite ABCD [Need Inverse Sine Function]
Find the unknown side and angle measures. Write and test the Logo code starting at point D. Note that Greek letters are used in Figure 14.3 to designate angle measures. The unit of measure is pixels.

Try to find the missing measures and Logo code BEFORE you look at the next page!
Kite One.png