Kites

Lesson #14 - Kites
Initial posting - July, 2011 as Lesson 11 Revision date - Fall 2017

** 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
 * 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.

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 PQRS ** Find 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!