I. On the staircase, the depth and height of each step is the same, x inches. What is the value of y in terms of x? ) ftJ'I-. 2. The center of the circle is 0 with diameter PQ. The two semicircles have diameters PO and OQ. The circumference of circle 0 is 64n. What is the length of the curved path from P to Q? C,41f = "r2 \,=8- J 3. Find the perimeter of the figure. ) 8 8 \ r: '? 4. SA is an arc of a circle with center Q. The length of the arc SA is 9Jr" What is the area of the sector SQA" ~ . (-:z.we> =C1(f ~.2-\\r=-q\T \2. .1.,-::::q (Q 5. Find the value of z and w. ) 2'1~50 'f ~2b \ =t=(oS '5\'<\ tot>:::: 6. Find the value of x and w. \5 ~ ~:~3 ::: ¥t \~=-\3.=t'l I J~. 7. In the cube. CE = sff. Find BC ot :) (}G \8c ~~ J - (S)2--r~5)2-= Co'-l +- \2"6" Gc.?- _--- = GG 2.- ( GC= l5'8 ] G<-2-=~2- s. P is the center ofthe circle and WAC is equilateral with side length 6. Find the area of the circle. BD == 3 (2f3t> -=- roJ \",5> =- '3Ji. '"2:" 3 -3 Name • Class Date _ Additional Practice 17 THE PYTHAGOREAN THEOREM Use after Section 9.3 Problem Set A In problems 1 and 2, use .6.ABC. 1 Complete each of the following. a If AD = 3 and BD = 5, b e d e f find CD. If AD = 5 and find AC. If BD = 9 and find BC. If AD = 5 and find BD. If AC = 2 vB find AB. AB = 7, AB = 16, CD = 5, C la ~' Ib~ ~ A \~ B Ie D ~" Id f.2 and AD = 4, fa \2 _ Ie If AD = 10 and BD = 8, If find BC. 2 JT5 Complete each of the following. AD AD AC BC a CD = BD b AC = e BC = AB d 6ABC-6 __ C e 6ADC-6_D_ c...,D 2a 2b ~ 2e A. A'f;> BD 2d-/lA'OC 2e t;..A:DC 3 L EFG = 90° FR is the altitude to EF = x Conclusion: (EH)(EG) = XZ E Given: CE. G 4 Given: 6JOM is a right 6. with right L at O. OK.1JM Prove: JO = x + 2 JK. JM = XZ Prove: J ~ . = K ~D-- 25 B ----~---(continues) 224 Additional Practice 17 '/..-r-2 M S p~ --S XC.1 ClJ CD is the altitude to AB. CD = 5 AD. DB '""T~ 0~ .J~ -=={f -t- 2)~:y.!-t~J+ + 4x + 4 A 5 Given: X+2 -J~ o Copyright @ McDougal, Littell & Company : ~ame Class Date Additional Practice 11 Use after Section 9.3 ~ THE PYTHAGOREAN THEOREM Problem Set B 6 Given: _ A LACB is a right angle. CD is altitude to AB. Show: 8 _ (AC)2 AD - AB B b BD = (BC)2 AB 7 LACB is a right angle. CD is altitude to All A AC 1. AD 8 If BC = 2' fmd BC' AD 4 . AC b If BD = 25' fmd BC' (Hint: Use the results of problem 6.) c Given: 78 7b \/l-l 215 _ B H Problem Set C 8 Find FG. 8 E 9 G If .6.ABC is a right triangle with altitude AD to hypotenuse Be and coordinates shown, find the coordinates of point A. B (-9,0) Copyright @ McDougal, Littell & Company y A D C (4,0) x Additional Practice 17 225 Name----------- • __ . class oute _ Additional Practice 18 Use after Section 9.7 THE PYTHAGOREAN THEOREM Problem Set A 1 2 3 4 5 A a AB = 15 Find BC and AC. b AC = 2 v3 Find BC and AB. c AC = 8~v3 Find BC and AB. 1a I 2 )~ ~. 5,1-=1- 1b B EF= V5 Find DE and DF. b DF = V'i7 Find EF and DE. c DE = 12 Find EF and DF. 1c a {\5 2IS 2a F I vJ?,T @2. ) 2b 30 0 o~ E 2c "2- L\S3 , SJ3 a GH= 1 Find HJ and GJ. b GH = 10 Find HJ and GJ. c HJ=4t Find GH and GJ. d HJ = V5 Find GH and GJ. 3a G ABCD is a rhombus. BD = 14 AC = 48 Find the perimeter of the rhombus. Y.5 3d Find the diagonal of a square if the length of a side is 2. 4 };jfJC A EG = 2EK EGHK is a rectangle. F and J are midpoints. EG = 10 Find FK. E B F ] L...1.5J1- J $,[\0 2&,, \00 G 6 K 6- 3c 45 ] J \D ) \Or-2- 0 H~ \ 3b 5 6 -:to 'Q -=t,5I3 50- H Problem Set B 7 Show that in a 30°-60°_90° triangle the bisector of the 60° angle divides the longer leg in the ratio of 1:2. 226 Additional Practice 18 Copyright @ McDougal. Littell & Company Name-------- • Class Date_. _ Additional Practice 18 THE PYTHAGOREAN THEOREM Use after Section 9.7 Problem Set B (continued) 8 9 \g a Find YZ. b Find XV. 8b e Find WY. 8e CoG d Find: Perimeter Perimeter 8d -5;3 W AXYW X 8a z Y AWYZ Write A for always, S for sometimes, or N for never. a If two isosceles right triangles have hypotenuses that coincide, then if a quadrilateral is formed, it is a rhombus. b In quadrilateral ABeD, Ls A and B are right angles and diagonal XC is longer than diagonal BD. Therefore, AD is longer than nc. e If the altitude on the hypotenuse of a right triangle divides the triangle into two 45°_45°_90°triangles, then the original triangle was isosceles. d The length of one-half a diagonal of a rhombus is equal to one-fourth the perimeter of the rhombus. " 9a _ 9b---Uge 9d f\ N _ Problem Set C U"~e.. ~j~j~(n 10 Show that 2x + 2, x2 + 2x, and x2 the sides of a right triangle. 11 Show that the only right triangle in which the lengths of the sides are consecutive integers is the 3, 4, 5 triangle. 12 In a 30°-60°.90° triangle, find the ratio of the product of the shorter leg and the altitude on the hypotenuse to the product of the longer leg and the hypotenuse. 12 _ If a 650-cm ladder is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the ladder be to the building? 13 ILto cxY\_ The lengths of the legs of a right triangle are x and 3x + y. The length of the hypotenuse is 4x - y. Find the ratio of x to y. 14 13 14 Copyright @ McDougal, Littell & Company + 2x + 2 generate ex) 2- + ()<. +\ ~2. =- ( )( *2 YL G;:1)~ Additional Practice 18 227
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