2
The P tha orean Theorem and Its Converse Notes Sheet Pythagorean Theorem B JV\ A (,'~h.t Is , r~C-Sl-1~ o~ +\.t~ sttlcarr-s (';)IS! +\"c I ell\~ \-~s e S; i-\- e \ t~ S \' s e...'z, L-t<\ \ + I) ~ \1 c ~t-'CAC...-£ a oS:- ~~L! \ !If\t) \~ o.~ t-It\~ ~ ~~o4 eV\lASC. 1. '2"Z 8 X ;- 17 -t-::; )( L.-- ).0 ~ tl{1 X V;:{~30"' f= Ij.(L] Guided Practice Find x. 1. 15 6 Your Turn 3. c A 2. 11 Pythagorean Triples Sc.~ S &~ -1'r.'<ee. ""C>~ l..~'("o w"'e>\e V\L-\~be€$ "StAt.."'- +~~~ o. ."2t-101 G < ~,l{)t; 5, III 13 s. lSI 17 =.«. ;;.S ~I -0 J 10 (0,'tl{,"J..b Jh / 30, 3Gt Il-C4~,t;o Cf,I'2}IS It;, 3&, 31 Zl,,{/ (.,{s) 5) ~ \ J 7). I 7') )'/.-, ~YI ~X ~)I. J '2)( ) (3>- t», I~~, IN 7" 'J J f-( 1- );Z 5~ [I '2;, X L1 q z: 1;21 =.}('"t8l X "1-~fiO X:::')M 4. x . 'Z- 'Q? -z.. fZ ~ 0 +X I t.(v[ ::. bL{ r-A z, f~O~ >-:-'-i-JS

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Page 1: lASC.mathwithmrslandrum.weebly.com/uploads/2/1/4/9/21496324/...The P tha orean Theorem and Its Converse Notes Sheet Pythagorean Theorem B JV\ A (,'~h.t Is , r~C-Sl-1~ o~ +\.t~ sttlcarr-s

The P tha orean Theorem and Its Converse Notes SheetPythagorean Theorem BJV\ A (,'~h.t Is , r~C-Sl-1~ o~ +\.t~ sttlcarr-s (';)IS! +\"cIell\~ \-~s e S; i- \- e \ t ~S \'s e...'z, L-t<\ \ + I) ~ \1 c ~t-'CAC...-£ aoS:- ~~L! \ !If\t) \~ o.~ t-It\~ ~ ~~o4 eV\lASC.

1. '2"Z 8X ;- 17 -t-::;)( L.-- ).0 ~ tl{1

XV;:{~30"'f= Ij.(L]

Guided PracticeFind x.1.

15

6

Your Turn3.

c A

2. 11

Pythagorean TriplesSc.~ S &~ -1'r.'<ee. ""C>~ l..~'("o w"'e>\e V\L-\~be€$ "StAt.."'- +~~~o.."2t-101G<

~,l{)t; 5, III 13 s. lSI 17 =.«. ;;.S~ I -0 J 10 (0,'tl{,"J..b Jh / 30, 3Gt Il-C4~,t;oCf,I'2}IS It;, 3&, 31 Zl,,{/ (.,{s) 5 ) ~ \ J 7). I 7'))'/.-, ~YI ~X ~)I. J '2)( ) (3>- t», I~~, IN 7" 'J J f-( 1- );Z 5~

[I '2;, X L1 q z:

1;21 =.}('"t8lX "1-~fiOX:::')M

4. x

. 'Z- 'Q? -z..fZ ~ 0 +X

It.(v[ ::. bL{ r-A z,

f~O~>-:-'-i-JS

Page 2: lASC.mathwithmrslandrum.weebly.com/uploads/2/1/4/9/21496324/...The P tha orean Theorem and Its Converse Notes Sheet Pythagorean Theorem B JV\ A (,'~h.t Is , r~C-Sl-1~ o~ +\.t~ sttlcarr-s

Guided PracticeUse a Pythagorean Triple to find x. Explain your reasoning.5. 6.

~ 1~7~::;~\2.:-~~ L(

x;;5-315 [X~J1J

c.""e G\L?

0( 'Z+ 1Z"t::::-15'1{tlyl-( ;;),15

7"l5 ;:)25Your Turn7.

14

48

£1~--:'f; /2Lo:'{~5X: l~.l{

0~t:~e~c..;

:l.

20 "f r-202=5"2

:230,(+40£>:' oZ 76'()"7D't---')..70 1./

V

x

)'b7.; 2'1'+10"<-676:- S76·t-l~b70 z: b 76

8.

x

24Converse of the Pythagorean Theorem

::r ~ ~ c +- v.,4:: c:'2 t\A eV\ \ ("''O.'l-'~\e \S ~ (")~'" -\- A.

Pythagorean Inequality to Prove Acute Triangles

1- S e2.L 4,.L +- b2 1-~eV\ L1 \....S e,c~ie I

Pythagorean Inequality to Prove Obtuse Triangles

10. 6.2, 13.8,20"

Guided PracticeDetermine whether each set of numbers can be the measures of a triangle. If to, classify the triangle as acute,right or obtuse. Justify your answer.9. 7, 14, 16

1·-r-\L\ tib .> 7+1b)lLf V ILl tl6! 1v'J. '" c:s a. .\-('\"0, ""'5\~

Ib7.? 1'\~1"2 J~5b J~b t!.{~ \~C;~ A

2t;b 7 ;( '<5~YourTurn

.r. 9, 12, 15 VorTI~)lr~ '1+\5/1'"2v 1..2+I.s>~

).s ~ h,.151..1 \').1.T'\~~j.S 'l1'i"t~1 ~" ., c t..l- Jl'