11.Making the Connection[Language]Qi qiaoispronounced [che–che–au.].22222222222424242222484CHAPTER 9The Pythagorean Theorem9.1
IMPROVING YOURVISUAL THINKINGSKILLSFold, Punch, and SnipA square sheet of paper is folded vertically, a hole is punched out of the center, and then one of the corners is snipped off.When the paper is unfolded it will look like the figure at right.Sketch what a square sheet of paper will look like when it is unfolded after the following sequence of folds, punches,and snips.Fold once.Fold twice.Snip double-fold corner.Punch opposite corner.12.Make a set of your own seven tangram pieces and create the Cat, Rabbit, Swan, andHorse with Rider as shown on page 484.13.Find the radius of circle Q.14.Find the length ofAC.15.The two rays are tangent to the circle. What’s wrong withthis picture?16.In the figure below, point A17.Which congruence shortcut 18.Identify the point ofis the image of point Aafter can you use to show that concurrency in QUOa reflection over OT.What ABPDCP?from the construction are the coordinates ofA?marks.19.In parallelogram QUID, mQ2x5°and mI4x55°. What is mU?20.In PRO, mP70°and mR45°. Which side of the triangle is the shortest?POBDACPAyBADCC12 units182 cm4, 4312.15.Draw radii CDand CB.ABCADC90°. Forquadrilateral ABCD 54°90°mC90°360°, somC126°.BD126° but126°226°360°.Exercises 19, 20, 18[Language]Thefigure names in these exercisesform a legal phrase:quid pro quo.Quid pro quo means “somethingfor something.”It’s used to meanthe consideration for a contract,that is, what each party gets outof it (such as money or advan-tage). A similar colloquialexpression is “tit for tat.”EXTENSIONHave students show algebraicallythat 3-4-5 is the only Pythagoreantriple of consecutive positiveintegers.LESSON 9.4Story Problems485IMPROVING VISUAL THINKINGSKILLS9.37.15.54.39.14.56.23.7
L E S S O N9.5486CHAPTER 9The Pythagorean TheoremWe talk too much; we shouldtalk less and draw more.JOHANN WOLFGANGVON GOETHEL E S S O N9.5Distance in CoordinateGeometryViki is standing on the corner of Seventh Street and 8th Avenue, and her brotherScott is on the corner of Second Street and 3rd Avenue. To find her shortest sidewalkroute to Scott, Viki can simply count blocks. But if Viki wants to know her diagonaldistance to Scott, she would need the Pythagorean Theorem to measure across blocks.You can think of a coordinate plane as a grid of streets with two sets of parallellines running perpendicular to each other. Every segment in the plane that is not in the x- or y-direction is the hypotenuse of a right triangle whose legs are in the x- and y-directions. So you can use the Pythagorean Theorem to find the distance between any two points on a coordinate plane.