ࡱ> a-.[\o S l  bjbj O |=pBB8le< R5555&& &XQZQZQZQZQZQZQ TVrZQi'P"Z&''ZQ55 Qa,a,a,'j55XQa,'XQa,a,nbJYTZM5?*"P)(jK DQQ0 RKW*W@ZMZMWN\&"&a,'*'&&&ZQZQ+&&& R''''W&&&&&&&&&B K: Section 4-1: Classifying Triangles SOL: None Objectives: Identify and classify triangles by angles Identify and classify triangles by sides Vocabulary: Scalene no sides are congruent Isosceles two sides are congruent Equilateral all sides are congruent Equiangular all angles are congruent Key Concepts:  EMBED PowerPoint.Show.8  Concept Summary: Triangles can be classified by their angles as acute, obtuse or right Triangles can be classified by their sides as scalene, isosceles or equilateral  EMBED PowerPoint.Show.8  Example 1: The triangular truss below is modeled for steel construction. Classify (JMN, (JKO, and (OLN as acute, equiangular, obtuse, or right.  Example 2: The frame of this window design is made up of many triangles. Classify (ABC, (ACD, and (ADE as acute, equiangular, obtuse, or right. Example 3: Identify the indicated triangles in the figure.  a. isosceles triangles b. scalene triangles c. right triangle d. obtuse triangle Example 4: Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 d and KM = 4d 13. Example 5: Find the measures of the sides of (ABC. Classify the triangle by sides  Reading Assignment: Section 4.2 Homework: pg 180-1: 5, 9, 13-18, 27 Section 4-2: Angles of Triangles SOL: None Objectives: Apply the Angle Sum Theorem Apply the Exterior Angle Theorem Vocabulary: Exterior Angle: is formed by one side of a triangle and the extension of another side Remote Interior Angle: interior angles not adjacent to the given exterior angle Corollary: a statement that can be easily proven using a particular theorem Theorems: Angle Sum Theorem: The sum of the measures of the angles of a triangle is 180. Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Corollaries: 1) the acute angles of a right triangle are complementary 2) there can be at most one right or obtuse angle in a triangle Concept Summary: The sum of the measures of the angles of a triangle is 180 The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles  EMBED PowerPoint.Show.8  Example 1: Find the missing angle measures.  Example 2: Find the measure of each numbered angle in the figure.  Example 3: Find the measure of each numbered angle in the figure.  Example 4: Find the measure of each numbered angle in the figure. Reading Assignment: Section 4.3 Homework: pg 188-9: 5-9, 18-23 Section 4-3: Congruent Triangles SOL: G.5 The student will a) investigate and identify congruence and similarity relationships between triangles; Objectives: Name and label corresponding parts of congruent triangles Identify congruence transformations Vocabulary: Congruent triangles have the same size and shape (corresponding angles and sides () Congruence Transformations: Slide (also know as a translation) Turn (also known as a rotation) Flip (also known as a reflection) Key Concepts: Two triangles are congruent, if and only if, their corresponding parts are congruent Order is important!!! Theorems: Properties of triangle congruence: Reflexive: %JKL ( %JKL Symmetric: if %JKL ( %PQR, then %PQR ( %JKL Transitive: if %JKL ( %PQR and %PQR ( %XYZ then %JKL ( %XYZ Concept Summary: Two triangles are congruent when all of their corresponding parts are congruent.  EMBED PowerPoint.Show.8  Example 1: A tower roof is composed of congruent triangles all converging toward a point at the top. Name the corresponding congruent angles and sides of (HIJ and (LIK Name the congruent triangles Example 2: The support beams on the fence form congruent triangles.  Name the corresponding congruent angles and sides of (ABC and (DEF. Name the congruent triangles.  Example 3: The vertices of (RST are R(-3, 0), S(0, 5), and T(1, 1). The vertices of (R(S(T ( are R((3, 0), S((0, -5), and T((-1, -1). Verify that (RST ( (R(S(T(. Name the congruence transformation for (RST and (R(S(T(. Reading Assignment: Section 4.4 Homework: pg 195-198: 9-12, 22-25, 40-42 Section 4-4: Proving Congruence SSS and SAS SOL: G.5 The student will b) prove two triangles are congruent or similar, given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs. Objectives: Use the SSS Postulate to test for triangle congruence Use the SAS Postulate to test for triangle congruence Vocabulary: Included angle: the angle formed by two sides sharing a common end point (or vertex) Key Concepts: Side-Side-Side (SSS) Postulate: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. Concept Summary: If all of the corresponding sides of two triangles are congruent, then the triangles are congruent (SSS). If two corresponding sides of two triangles and the included angle are congruent, then the triangles are congruent (SAS).  EMBED PowerPoint.Show.8  Example 1: Write a two-column proof to prove that (ABC (GBC if GB ( AB and AC ( GC Statement Reasons Example 2: Write a flow proof. Given:C is midpoint of DB; (ACB ( (ACD Prove: "ABC ( "ADC Example 3: Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible A. B.  C. D.  a. ______ b. ______ c. ______ d. ______ Reading Assignment: Section 4.5 Homework: pg 203 - 206: 6-8, 17, 22-25, 33-34 Section 4-5: Proving Congruence ASA and AAS SOL: G.5 The student will b) prove two triangles are congruent or similar, given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs. Objectives: Use the ASA Postulate to test for triangle congruence Use the AAS Theorem to test for triangle congruence Vocabulary: Included side: the side in common between two angles (end points are the vertexes) Key Concepts: Angle-Side-Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Angle-Side (AAS) Theorem: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the triangles are congruent. Concept Summary: If two pairs of corresponding angles and the included sides of two triangles are congruent, then the triangles are congruent (ASA). If two pairs of corresponding angles and a pair of corresponding non-included sides of two triangles are congruent, then the triangles are congruent (AAS).  EMBED PowerPoint.Show.8  Section 4-4 & 5: Congruent Triangles Concept Summary: Known PartsDefinitionAble to determine congruency?ReasonSSSYou know that all three sides of one triangle are equal to the corresponding three sides of another triangleYesSSS postulateSASYou know that two sides and the angle between those two sides are equal to the corresponding two sides and included angle of another triangleYesSAS postulateASAYou know that two angles and the side included between those two angles are equal to the corresponding two angles and included side of another triangleYesASA postulateAASYou know that two angles and one side not included between those angles are equal to the corresponding two angles and non-included side of another triangleYesAAS Theorem (4.5) Can get it into form of ASA, since other angle must also be congruent (sum of triangles angles = 180)SAAYou know that one side and two angles which do not include that side are equal to the corresponding side and non-included angles of another triangleYesCan get it into form of ASA, since other angle must also be congruent (sum of triangles angles = 180)ASSYou know that one angle and two sides which do not include that angle are equal to the corresponding angle and two non-included sides of another triangleNoMight be congruent, but cannot prove with given informationSSAYou know that two sides and a non-included angle are equal to the corresponding two sides and non-included angle of another triangleNoMight be congruent, but cannot prove with given informationAAAYou know that all three angles of one triangle are equal to the corresponding three angles of another triangleNoSides are proportional (think concentric triangles) Example 1: Write a paragraph proof Given: L is the midpoint of WE and WR // ED Prove: "WRL ( "EDL  Example 2: Write a flow proof Given: (NKL ( (NLM and KL(JM Prove: LN ( MN Example 3: Write a flow proof. Given: (ADB ( (ACE and EC ( BD Prove: (AEC ( (ABD Example 4: The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each uses the same amount of material, 17 inches. Determine whether (ABE ( (CBD. Justify your answer. Reading Assignment: Section 4.6 Homework: pg 211 - 212: 15-20 all in two-column proof format Section 4-6: Isosceles Triangles SOL: None. Objectives: Use properties of isosceles triangles Use properties of equilateral triangles Vocabulary: Vertex angle the angle formed by the two congruent sides Base angle the angle formed by the base and one of the congruent sides Theorems: Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollaries: A triangle is equilateral if, and only if, it is equiangular. Each angle of an equilateral triangle measures 60. Key Concepts:  EMBED PowerPoint.Show.8  Concept Summary: Two sides of a triangle are congruent if, and only if, the angles opposite those sides are congruent. A triangle is equilateral if, and only if, it is equiangular. Example 1: Write a two-column proof Given: AB = BC = BD (ACB ( (BCD Prove: (A ( (D Statement Reason Example 2: If DE ( CD, BC ( AC and m(DCE = 120(, what is the measure of (BAC?  45.5 57.5 68.5 75 Example 3: If AB ( BC, AC ( CD, m(ABC = 80(, what is the measure of (ADC? 25 35 50 130  Example 4: Name two congruent angles Name two congruent segments  Example 5: (ABC is an equilateral triangle. AD bisects (BAC Find x Find m(ADB Reading Assignment: Section 4.7 Homework: pg 219 - 20: 9, 10, 13-18, 27 Section 4-7: Triangles and Coordinate Proof SOL: G.5 The student will b) prove two triangles are congruent or similar, given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs. Objectives: Position and label triangles for use in coordinate proofs Write coordinate proofs Vocabulary: Coordinate Proof: Uses figures in the coordinate plane and algebra to prove geometric concepts. Key Concepts: Use the origin as a vertex or center of the figure Place at least one side of a polygon on an axis Keep the figure within the first quadrant if possible Use coordinates that make computations as simple as possible Concept Summary: Coordinate proofs use algebra to prove geometric concepts. The distance formula, slope formula, and midpoint formula are often used in coordinate proofs.  EMBED PowerPoint.Show.8  Example 1: Name the missing coordinates of isosceles right triangle QRS. Example 2: Name the missing coordinates of isosceles right (ABC Example 3: Write a coordinate proof to prove this flag is shaped like an isosceles triangle. The length is 16 inches and the height is 10 inches Reading Assignment: reread chapter 4 Homework: Chapter Review handout Lesson 4 -1: Refer to the figure.  1. What is the special name given to the pair of angles shown by (2 and (6? 2. Find m(3. 3. Find m(4. 4. Find the slope of the line that contains the points at (4, 4) and (2, 5). 5. Write the equation of a line in slope-intercept form that has a slope of and contains the point at (0, 5). 6. What is the slope of a line that is perpendicular to the line y = 2/3x 5? a. -3/2 b. -2/3 c. 2/3 d. 3/2  Lesson 4 -2: Refer to the figure. 1. Classify (RST as acute, equiangular, obtuse, or right. 2. Find y if (RST is an isosceles triangle with RS ( RT. Refer to the figure. 3. Find x if (ABC is an equilateral triangle. 4. Name the right triangles if AD ( CB. 5. Classify (MNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15. 6. Choose the angle measures that represent the angles of an obtuse triangle. a. 45,45,90 b. 60,60,60 c. 50,60,70 d. 30,50,100 Lesson 4 -3: Find the measure of each angle. 1. m(1 2. m(2 3. m(3 4. m(4 5. m(5 6. Two angles of a triangle measure 46( and 65(. What is the measure of the third angle? a. 65( b. 69( c. 111( d. 115( Lesson 4 -4 :Refer to the figure. 1. Identify the congruent triangles. 2. Name the corresponding congruent angles for the congruent triangles. 3. Name the corresponding congruent sides for the congruent triangles. Refer to the figure. 4. Find x. 5. Find m(A. 6. Find m(P if (OPQ ( (WXY and m(W = 80(, m(X = 70(, m(Y = 30(. a. 30( b. 70( c. 80( d. 100( Lesson 4 -5: Determine which postulate can be used to prove that the triangles are congruent. 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(A ( (R b. (C ( (T c. (A ( (T d. (B ( (S  Lesson 4 -6: Refer to the figure. Complete each congruence statement and the postulate or theorem that applies. 1. (WXY ( (_____ by _____. 2. (WYZ ( (_____ by _____.  3. (VWZ ( (_____ by _____. 4. What additional congruence statement is necessary to prove (RST ( (UVW by the ASA Postulate? a. (T ( (W b. (R ( (U c. ST ( UW d. RT ( VW Lesson 4 -7: Refer to the figure.  1. Name two congruent segments if (1 ( (2. 2. Name two congruent angles if RS ( RT. 3. Find m(R if m(RUV = 65(. 4. Find m(C if (ABC is isosceles with AB ( AC and m(A = 70(. 5. Find x if (LMN is equilateral with LM = 2x 4, MN = x + 6, and LN = 3x 14. 6. 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Ldall angles    % ( Rp@Times New Roman0c fh0 |@{TiK0W0fh|0PU0z08gl~0$~@{!0l`pm50l r(@{,<dv%    Td_5MKKKAJA_ILT< 90   % ( Rp@Times New RomanW0fhL|PQ|Hm|c XX0$~@{0PU0z08gm50l (@{,<dvR!\P|p|m|||dv%    TT5MKKKAJAILP  % ( F(GDIC5vFGDICRp@Times New Roman0( \m0 m0PU0z08g 8t @{8 0@{ 0$l`pm50lq(@{(dv%    TD~KKKAJAD LdMeasure of    % ( Rp@Times New Roman0c #fg0 @{ TiK0W0fg0PU0z08gX~ 0$~@{!0l`pm50lq(@{(dv%    TMKKKAJAM L`one angle    % ( Rp@Times New Roman0 fh0 |@{TiK0W0fh|0PU0z08gl~0$~@{!0l`pm50l r(@{,<dv%    Td`KKKAJA`LT> 90   % ( Rp@Times New RomanW0fhL|PQ|Hm| XX0$~@{0PU0z08gm50l (@{,<dvR!\P|p|m|||dv%    TTKKKAJALP  % ( F(GDICFMFGDICRp@Times New Roman0c ,fg0 @{TiK0W0fg0PU0z08gX~ 0$~@{!0l`pm50lq(@{(dv%    T|bUmKKKAJAbiL\No sides    % ( Rp@Times New Roman0 fg0 @{ TiK0W0fg0PU0z08gX~ 0$~@{!0l`pm50lq(@{(dv%    TZpKKKAJAZ L`congruent  % ( F(GDICGFGDICRp@Times New Roman0c 3fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq(@{(dv%    TxlKKKAJAlL\2 sides    % ( Rp@Times New Roman0 fg0 @{ TiK0W0fg0PU0z08gX~ 0$~@{!0l`pm50lq(@{(dv%    T\KKKAJA\  L`congruent  % ( F(GDICDFGDICRp@Times New Roman0c :fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq(@{(dv%    TxhKKKAJAhL\3 sides    % ( Rp@Times New Roman0 fg0 @{ TiK0W0fg0PU0z08gX~ 0$~@{!0l`pm50lq(@{(dv%    TXKKKAJAX L`congruent  % ( F(GDIC=FXLEMF+*@$?? @$ljCCB 1B!b $$==% % V0<% % $$AAFEMF+@<0VUU?A@<0ljCCljCНC9CНC9CC@: $$==_888 % % V, H% % $$AA( : " FEMF+@ FGDICRp@Times New Roman0c Bfg0 |@{TiK0W0fg|0PU0z08gX~0$~@{!0l`pm50lq(@{(dv%    Tl2t4KKKAJA2/LXRight  % ( F(GDICFXLEMF+*@$?? @$ljCU-CB 1B!b $$==% % V0% % $$AAFEMF+@<0VUU?A@<0ljCU-CljC9fC9C9fC9CU-C@: $$==_888 % % V, % % $$AA( : " FEMF+@ FGDICRp@Times New Roman0 fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    Tp)}KKKAJA)LXObtuse   % ( F(GDIC>FXLEMF+*@$?? @$ljCU)DB 1B!b $$==% % V0=!##!!% % $$AAFEMF+@<0VUU?A@ <0ljCU)DljCED9CED9CU)D@ : $$==_888 % % V, I!##!% % $$AA( : " FEMF+@ FGDICRp@Times New Roman0c Kfg0 |@{TiK0W0fg|0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    Tl1u6KKKAJA11LXAcute   % ( F(GDIC]FXLEMF+*@$?? @$#D9CB 1B!b $$==% % V0](( 0 0(% % $$AAFEMF+@ <0VUU?A@ <0#D9C#DOC@DOC@D9C@  : $$==_888 % % V,Q(( 0 0% % $$AA( : " FEMF+@ FGDICRp@Times New Roman04\m0m0PU0z08g8t@{8 0@{0$l`pm50lq(@{(dv%    TxdKKKAJA~L\Scalene    % ( F(GDICFXLEMF+*@$?? @$!DiCp|B1B!b $$==% % V0t(t(m 0m 0t(% % $$AAFEMF+@ <0VUU?A@ <0!DiC!DUD@DUD@DiC@  : $$==_888 % % V,{t(t(m 0m 0% % $$AA( : " FEMF+@ FGDICRp@Times New Roman04\m0 m0PU0z08g8t@{8 0@{0$l`pm50lq (@{( dv%    TKKKAJA L`Isosceles    % ( F(GDIC_FXLEMF+*@$?? @$D#Dp"C 1B!b $$==% % V0_%(%+ 0+ 0(%(% % $$AAFEMF+@<0VUU?A@<0D#DD8.D@D8.D@D#D@: $$==_888 % % V,S%(%+ 0+ 0(% % $$AA( : " FEMF+@ FGDICRp@Times New Roman04 \m0 m0PU0z08g 8t @{8 0@{ 0$l`pm50lq(@{(dv%    TmKKKAJAm LdEquilateral  % ( F(GDICFXLEMF+*@$?? @$ljC9^#D:,C 1B!b $$==% % V0(+V+V((% % $$AAFEMF+@<0VUU?A@<0ljC9^#DljCz.DCz.DC9^#D@: $$==_888 % % V, (+V+V(% % $$AA( : " FEMF+@ FGDICRp@Times New Roman04 \m0 m0PU0z08g 8t @{8 0@{ 0$l`pm50lq (@{( dv%    T%KKKAJA% LdEquiangular   % ( F(GDICFGDICRp@Times New Roman|/0  @{m \/00PU0z08gm0m4 l`pm50lTqw(@{wdv%    TKKKAJA Ld3 congruent   % ( Rp@Times New Roman0c cfg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq(@{(dv%    TpKKKAJALXangles   % ( F(GDICJFEMF+*@$??@th UC)DCqp,DC(+D D(+D Dqp,DD)D DUQ'D D(DC(DCUQ'D@( !b $$=='̙%  % VDH q*+*#*#+y$q*#)#**)%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % VDJ q*+*#*#+y$q*#)#**)% % $$AA( " FEMF+@ FGDICF(GDICl(FEMF+*@$??@l` TbDC`D8}C@bD8}C@bD&?C[[D&?C[[DqL2C"cDqL2C"cD8}CmdD8}C@!b $$==%  % V@l$ 866888 6 6 8 89%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V@k% 866888 6 6 8 89% % $$AA( " FEMF+@ FGDICF(GDIClLFEMF+*@$??@XLGD9CGD-CqRD-CqRD9CGD9CGDCU9DDtC@!b $$==%  % V8mK1144111g%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V8kL1144111g% % $$AA( " FEMF+@ FGDICF(GDICLFEMF+*@$??@XLGDU}CGDCqRDCqRDUSCGDUSCGDCU9DD C@!b $$==%  % V8K1h144C1C11%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V8L1h144C1C11% % $$AA( " FEMF+@ FGDICF(GDICLFEMF+*@$??@XLGD&DGD'DURD'DURDB*DGDB*DGDe+D9.DDq)D@!b $$==%  % V8K1)1)4)4*1*1*1@*%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V8L1)1)4)4*1*1*1@*% % $$AA( " FEMF+@ FGDICF(GDIC1FEMF+*@$??@XLimCr\CimCǣCrACǣCrACr2CimCr2CimCyC{CC@!b $$==%  % V8/   V%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V80   V% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@XLV=mCxCV=mCUCACUCACNCV=mCNCV=mCUCr{CC@!b $$==%  % V8  9%  % $$AAF`TEMF+@@4^UU?A@$$==_888% % V8  9% % $$AA( " FEMF+@ FGDICF(GDIC/FEMF+*@$??@ XLV=mCǭDV=mCrDACrDAC DV=mC DV=mCr< Dr{CD@ !b $$==%  % V8-!! ! 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PD|p|m|||dv!PD|p|m|||dv%    TTKKKAJALP2  % ( Rp@Times New Roman P@|J Q|Hm|B KK! PD|p|0PU0z080idv! PD|p|m|||dv!PD|p|m|||dv%    T`KKKAJALT+ (  % ( Rp@Times New Roman P@|J Q|Hm|B KK! PD|p|0PU0z08idv! PD|p|m|||dv!PD|p|m|||dv%    TTKKKAJALP-  % ( Rp@Times New Roman P@|J Q|Hm|B KK! PD|p|0PU0z08Hjdv! PD|p|m|||dv!PD|p|m|||dv%    TXKKKAJALP6)  % ( Rp@Times New Roman P@|J Q|Hm|B KK! PD|p|0PU0z08jdv! PD|p|m|||dv!PD|p|m|||dv%    TT!KKKAJALP2  % ( Rp@Times New Roman0 /fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    F TdFqKKKAJAFLT=    TTrKKKAJAFLP"  TxKKKAJAFL\64 + 36  % ( Rp@Times New Roman0B fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    F0 TdFq7KKKAJAF0LT=    TTr7KKKAJAF0LP"  T`7KKKAJAF0LT100  % ( Rp@Times New Roman0B <fg>0#0-Zts~g0PU0z08gT0I0i0-Z@{dvdv@Times New Roman 6dv%    TpF;_KKKAJAFXLX= 10  % ( F(GDIC*FGDICRp@Times New Roman0 J<fX~>0#0-7ts~X~0PU0z08gT0I0i0-7@{dvdv4~0l,8~4~\t(0dv%    Tp3rWKKKAJAPLXDC =  % ( Rp@Times New Romants~X~@|J Q|Hm|B KKI0i0-70PU0z08g~0l 4~\t(0dv4~!PD|p|m|||dv%    TTs3WKKKAJAsPLP" % ( Rp@Times New Romani0-@|J Q|Hm|B KK~0l 4~\t0PU0z08hdv~! PD|p|m|||dv4~!PD|p|m|||dv%    T`3WKKKAJAPLT(3  % ( Rp@Times New Roman @|J Q|Hm|B KK~! PD|p|0PU0z08hdv~! PD|p|m|||dv4~!PD|p|m|||dv%    TT3WKKKAJAPLP  % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z080idv~! PD|p|m|||dv4~!PD|p|m|||dv%    TX3WKKKAJAPLP2)  % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z08idv~! PD|p|m|||dv4~!PD|p|m|||dv%    TT2JKKKAJAFLP2  % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z08Hjdv~! PD|p|m|||dv4~!PD|p|m|||dv%    Tl38WKKKAJAPLX+ (9   % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z08jdv~! PD|p|m|||dv4~!PD|p|m|||dv%    TT93IWKKKAJA9PLP  % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z08`kdv~! PD|p|m|||dv4~!PD|p|m|||dv%    TXR3mWKKKAJARPLP2)  % ( Rp@Times New Roman P@|J Q|Hm|B KK~! PD|p|0PU0z08kdv~! PD|p|m|||dv4~!PD|p|m|||dv%    TTn2xJKKKAJAnFLP2  % ( Rp@Times New Roman0B <fj>0#0-7ts~j0PU0z08gT0I0i0-7@{dvdv@Times New Roman Ydv%    TTR[dKKKAJARxLP= % ( Rp@Times New Romants~j@|J Q|Hm| ZKKI0i0-70PU0z08h @Times New Ro Ydv!PD|p|m|||dv%    vx TTv[KKKAJAvxLP"  T`[KKKAJAvxLT(1)    % ( Rp@Times New Romani0-@|J Q|Hm| [KK 0PU0z080idv! PD|p|m|||dv!PD|p|m|||dv%    TXZrKKKAJAnLP2  % ( Rp@Times New Roman @|J Q|Hm| \KK! PD|p|0PU0z08idv! PD|p|m|||dv!PD|p|m|||dv%    Tl[KKKAJAxLX+ (7)   % ( Rp@Times New Roman P@|J Q|Hm| ]KK! PD|p|0PU0z08Hjdv! PD|p|m|||dv!PD|p|m|||dv%    TTZ rKKKAJAnLP2  % ( Rp@Times New Roman0B fg0 @{TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    S T`SvKKKAJASLT=    TTwKKKAJASLP"  TpKKKAJASLX1 + 49  % ( Rp@Times New Roman0 dfg0 @{ TiK0W0fg0PU0z08gX~0$~@{!0l`pm50lq (@{( dv%    S T`SvKKKAJASLT=    TTwKKKAJASLP"  TXKKKAJASLP50  % ( F(GDICFGDICRp@Times New Roman0:\m0m0PU0z08g8t@{8 0@{0$l`pm50lq (@{( dv%     TKKKAJA LdDC = EC, so    TTKKKAJALP%!  TKKKAJALpDEC is isosceles        % ( F(GDICFEMF+*@$??@6@4^UU?A@7, C:CC:C@76!b $$==_888% % W$2  % % $$AA( " FEMF+@ FGDICF(GDIC14FEMF+*@$??@8@4^UU?A@9, 9C D C D@98!b $$==_888% % W$04S # #% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@:@4^UU?A@;, DU5CUcDU5C@;:!b $$==_888% % W$}'8% % $$AA( " FEMF+@ FGDICF(GDIC!FEMF+*@$??@<@4^UU?A@=, CCCC@=<!b $$==_888% % W$!% % $$AA( " FEMF+@ FGDICF(GDICZ%\FEMF+*@$??@>@4^UU?A@?, 9CDUՑCD@?>!b $$==_888% % W$Y%]S%3%% % $$AA( " FEMF+@ FGDICF(GDIC$FEMF+*@$??@@4^UU?A@, H!DCHDC@!b $$==_888% % W$%K(*2% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@@4^UU?A@, 9CUUC9fCUUC@!b $$==_888% % W$!#a#% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@@4^UU?A@,  CU DmCU D@!b $$==_888% % W$$($(% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@@4^UU?A@, !DPC:DPC@!b $$==_888% % W$[(.% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@@4^UU?A@ , 9C Cr|*C C@ !b $$==_888% % W$! % % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@ @4^UU?A@ ,  C*D1C*D@  !b $$==_888% % W$* *% % $$AA( " FEMF+@ FGDICF(GDICFEMF+*@$??@ @4^UU?A@ , !DUD0DUD@  !b $$==_888% % W$[(!,!% % $$AA( " FEMF+@ FGDICF4(EMF+*@$??!b Ld)??" FEMF+@  dO)"Microsoft PowerPoint PresentationMSPresentationPowerPoint.Show.89q %_) Chris HeadleeChris HeadleeOh+'0 `h  PowerPoint PresentationObjInfoJNPicturesCurrent UserMPGSummaryInformation(@oweoweChris Headleese4riMicrosoft PowerPointon@ $ @@0G՜.+,0    UOn-screen Shown-s5): Times New RomanDefault DesignClassifying TrianPowerPoint Document(OQ 5)DocumentSummaryInformation81Table- ]WSummaryInformation(T                        ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  ( / 0LDTimes New Roman0B 0@ .  @n?" dd@  @@`` 8<g 0AA@3 ʚ;ʚ;g4dddd B 0ppp@ <4dddd8pC 0t̟80___PPT10 cClassifying Triangles  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> *"(    6Xɉ P  T Click to edit Master title style! !  0`f   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0 c $DT T DTB ? c $D  DTB @ c $D  DTB A c $Dt t DTB B c $D  DTB C c $D4 4 DTB D c $D  DTB E c $D  DTB F c $DT T DTB G c $D  DTB H c $DDXB K 0Do::XB L 0DolmpR2 M s *R2 N s *\5R2 O s *oJ P <TSK  8Find the measures of the sides of %DEC. Classify the triangle by its sides. D (3, 9) E (3, -5) C (2, 2) *z # V Q <$  5E  R <x 5D  S <i9 5C  T <{ 5y  U <}Z 5x  V <h:b[  ^EC = " (-5  2)2 + (3  2)2 = "(-7)2 + (1)2 = "49 + 1 = "50V      W <) Z  rED = " (-5  3)2 + (3  9)2 = "(-8)2 + (-6)2 = "64 + 36 = "100 = 10e    . 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