Quadrilaterals and Polygons: Trapezoids and Kites

Section Warm up Section Warm-Up

Let’s make sure we are ready for this section by reviewing some of the concepts you have learned in previous sections.  All of these concepts will be used in this section, so be sure you are familiar with them.

think icon Think & Click: Exterior Angles in a Polygon

Now, you try. Complete the Think & Click activity by looking at the problem below, thinking about it, and then clicking on the question to reveal the solution.

If line l and line m are parallel, what can you say about angle 1 and angle 2?
 

Parallel lines l and m with transversal, angle 1 is below and to the right of the top line and angle 2 is above and to the right of the bottom line."/>

Angle 1 and angle 2 are consecutive angles, they are supplementary, the sum of their measures equals 180°.
 

If angle A and angle B are supplementary and angle A measures (3x – 15)° and angle B measures (2x + 40)°. Find the measure of each angle.
 

(3x – 15) + (2x + 40) = 180

5x + 25 = 180

5x = 155

x = 31

measure of angle A equals three times thirty one minus fifteen equals seventy eight degrees measure of angle B equals two time thirty one plus forty equals one hundred two degrees

Find the length of the hypotenuse of a right triangle if the legs have lengths 10 and 14, respectively.

Use the Pythagorean Theorem

102 + 142 = c2

100 + 196 = c2

296 = c2

c = 17.2



What is the sum of the angles in any quadrilateral?
 

A quadrilateral has four sides.

Sum of angles = (n – 2)•180° = (4 – 2)•180° = 360°