Unit 4 Day by Day Day Sections and Objectives Homework ?· Unit 4 Day by Day Day Sections and Objectives…

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<ul><li><p>1 </p><p>Unit 4 Day by Day </p><p>Day Sections and Objectives Homework </p><p>Monday </p><p>October 26 </p><p>U4D1 </p><p>4.2 and 4.9 Packet Pages 1-3 </p><p>Types of triangles, isosceles and </p><p>equilateral triangles </p><p>Page 228 (23-31, 35-37) </p><p>Page 288 (5-10, 17-20, 22-26) </p><p>Wednesday </p><p>October 28 </p><p> Day </p><p>U4D2 </p><p>4.3 and 4.4 Packet Pages 4-7 </p><p>Sum of interior angles of a triangle </p><p>Exterior Angel Theorem </p><p>Congruent Triangles </p><p>Page 236 (19-24, 41-44) </p><p>Page 242 (11, 17-19, 23-25, 31-34) </p><p>Friday </p><p>October 30 </p><p>U4D3 </p><p>4.5-4.7 Packet Pages8-15 </p><p>SSS, SAS, AAS, ASA, HL, CPCTC </p><p>Finish Packet Pages 11-15 </p><p>Tuesday </p><p>November 3 </p><p>U4D4 </p><p>Quiz 4.2-4.4 and 4.9 </p><p>Review </p><p>Page 247 (5-17 </p><p>Page 288 (13-16, 42-44) </p><p>Wednesday </p><p>November 4 </p><p>U4D5 </p><p>Review Packet Pages8-15 </p><p>Friday </p><p>November 6 </p><p>U4D6 </p><p>Quiz 4.2-4.9 </p><p>Review </p><p>Tuesday </p><p>November 10 </p><p>U4D7 </p><p>Test Unit 4 </p><p>None </p></li><li><p>2 </p><p>Chapter 4 Congruent Triangles </p><p>4.2 and 4.9 Classifying and Angle Relationships within Triangles. </p><p>Isosceles triangles are triangles with two congruent sides. </p><p> The two congruent sides are called legs. </p><p> The third side is the base. </p><p> The two angles at the base are called base angles. </p></li><li><p>3 </p><p>Match the letter of the figure to the correct vocabulary word in Exercises 14. </p><p> 1. right triangle __________ </p><p> 2. obtuse triangle __________ </p><p> 3. acute triangle __________ </p><p> 4. equiangular triangle __________ </p><p>Classify each triangle by its angle measures as acute, equiangular, right, or obtuse. (Note: Give two </p><p>classifications for Exercise 7.) </p><p> 5. 6. 7. </p><p>For Exercises 810, fill in the blanks to complete each definition. </p><p> 8. An isosceles triangle has ____________________ congruent sides. </p><p> 9. An ____________________ triangle has three congruent sides. </p><p> 10. A ____________________ triangle has no congruent sides. </p><p>Classify each triangle by its side lengths as equilateral, isosceles, or scalene. (Note: Give two </p><p>classifications in Exercise 13.) </p><p> 11. 12. 13. </p><p>Find the side lengths of the triangle. </p><p> 14. AB ____________________ AC ___________________ BC ______________ </p><p>15. Given: ABC is isosceles with base AB ; EBDA Prove: EBCDAC </p><p>16. In isosceles PQR, P is the vertex angle. If mQ = 8x 4 and mR = 5x + 14, find the mP. </p><p>17. In isosceles triangle CAT, C is the vertex angle. If A = 8x 4 and mT = 5x + 14, then what is the </p><p>measure of C? </p></li><li><p>4 </p><p> 3. mX __________ 4. BC __________ mA __________ </p><p> 5. PQ __________ 6. mK __________ t __________ </p></li><li><p>5 </p><p>4.3 and 4.4 Angle Relationships and Congruent Triangles. </p><p> The interior is the set of all points inside the figure. The exterior is the set of all points </p><p>outside the figure. </p><p> An interior angle is formed by two sides of a triangle. </p><p> An exterior angle is formed by one side of the triangle and extension of an adjacent side. </p><p> Each exterior angle has two remote interior angles. A remote interior angle is an </p><p>interior angle that is not adjacent to the exterior angle. </p></li><li><p>6 </p><p>Congruent Triangles: Two s are if their vertices can be matched up so that corresponding angles and sides of the s are . </p><p>Congruence Statement: RED FOX </p><p>List the corresponding s: corresponding sides: </p><p>R ___ RE ____ </p><p>E ___ ED ____ </p><p>D ___ RD ____ </p><p>Examples: </p><p>1. The two s shown are . </p><p>a) ABO _____ b) A ____ </p><p>c) AO _____ d) BO = ____ </p><p>2. The pentagons shown are . </p><p>a) B corresponds to ____ b) BLACK _______ </p><p>c) ______ = mE d) KB = ____ cm </p><p>e) If CA LA , name two right s in the figures. </p><p>3. Given BIG CAT, BI = 14, IG = 18, BG = 21, CT = 2x + 7. Find x. </p><p>The following s are , complete the congruence statement: </p><p>4. YWZ_______ </p><p>5. MQN _______ </p><p>6. WTA ________ </p><p>Parts of a Triangle in terms of their relative positions. </p><p>7. Name the opposite side to C. </p><p>8. Name the included side between A and B. </p><p>9. Name the opposite angle to BC . </p><p>D C </p><p>O </p><p>B A </p><p>B </p><p>L A </p><p>C </p><p>K </p><p>H </p><p>O </p><p>R </p><p>S </p><p>Y X </p><p>Z W M N O </p><p>P Q W </p><p>A </p><p>C </p><p>H T </p><p>A </p><p>B C </p><p>4 cm </p><p>E </p></li><li><p>7 </p><p>10. Name the included angle between AB and AC . State whether the pairs of figures are congruent. Explain. </p><p>Exterior Angles: Find each angle measure. </p><p> 37. mB ___________________ 38. mPRS ___________________ </p><p> 39. In LMN, the measure of an exterior angle at N measures 99. </p><p>1m</p><p>3L x </p><p> and 2</p><p>m3</p><p>M x . Find mL, mM, and mLNM. ____________________ </p><p> 40. mE and mG __________________ 41. mT and mV ___________________ </p><p> 42. In ABC and DEF, mA mD and mB mE. Find mF if an exterior </p><p>angle at A measures 107, mB (5x 2) , and mC (5x 5) . _______________ </p><p> 43. The angle measures of a triangle are in the ratio 3 : 4 : 3. Find the angle measures of the triangle. </p><p> ____________________ </p><p>44. One of the acute angles in a right triangle measures 2x. What is the measure of the other acute angle? </p><p>___________________ </p></li><li><p>8 </p><p>45. The measure of one of the acute angles in a right triangle is 63.7. What is the measure of the other acute angle? </p><p>_______________________ </p><p>46. The measure of one of the acute angles in a right triangle is x. What is the measure of the other acute angle? </p><p>_________________________ </p><p>47. Find mB 48. Find m</p></li><li><p>9 </p><p>4.5 4.7 Proving Triangles are congruent Ways to Prove s : </p><p>SSS Postulate: (side-side-side) Three sides of one are to three sides of a second , </p><p>Given: AS bisects PW ; AWPA </p><p>SAS Postulate: (side-angle-side) Two sides and the included angle of one are to two sides </p><p> and the included angle of another . </p><p>Given: PX bisects AXE; XEAX </p><p>ASA Postulate: (angle-side-angle) Two angles and the included side of one are to two angles </p><p> and the included side of another . </p><p>Given: MHAT</p><p>THMA</p><p>//</p><p>// </p><p>AAS Theorem: (angle-angle-side) Two angles and a non-included side of one are to two </p><p> angles and a non-included side of another . </p><p>Given: CAtsbiUZ sec </p><p> ZAUZCUUZ ; </p><p>HL Theorem: (hypotenuse-leg) The hypotenuse and leg of one right are to the hypotenuse </p><p> and leg of another right . </p><p>Given: FCAT </p><p> Isosceles FAC with legs ACFA, </p><p>CPCTC: Corresponding parts of congruent triangles are congruent </p><p>A </p><p>P W S </p><p>A </p><p>X </p><p>P </p><p>E </p><p>A </p><p>M </p><p>T </p><p>H </p><p>C </p><p>R U Z </p><p>A </p><p>A </p><p>F T C </p></li><li><p>10 </p><p> s SSS, SAS, ASA, AAS, or HL </p><p>State which congruence method(s) can be used to prove the s . If no method applies, write none. All markings must </p><p>correspond to your answer. </p></li><li><p>11 </p><p>Fill in the congruence statement and then name the postulate that proves the s are . If the s are not , write not possible in second blank. (Leave first blank </p><p>empty) *Markings must go along with your answer** </p></li><li><p>12 </p><p>#1 Given: USUTSRUTSR ;//; Prove: UVST // </p><p>1. USUTSRUTSR ;//; 1. _____________________________ </p><p>2. 1 4 2. __________________________________________ </p><p>3. RST TUV 3. __________________________________________ </p><p>4. 3 2 4. __________________________________________ </p><p>5. UVST // 5. __________________________________________ </p><p>#2 Given: D is the midpoint of CBCAAB ; Prove: CD bisects ACB. </p><p>1. D is the midpoint of CBCAAB ; 1. _________________________________________ </p><p>2. DBAD 2. __________________________________________ </p><p>3. CDCD 3. __________________________________________ </p><p>4. ACD BCD 4. __________________________________________ </p><p>5. 1 2 5. __________________________________________ </p><p>6. CD bisects ACB. 6. __________________________________________ </p><p>#3 Given: AR AQ; RS QT Prove: AS AT </p><p>1. AR AQ; RS QT 1. ________________________ </p><p>2. </p></li><li><p>13 </p><p>Fill in Proofs: </p><p>#1 </p><p>Given: AB CB </p><p> AC BD </p><p>Prove: ADB CDB </p><p>1. AB CB 1. _________________________________________________ </p><p>2. AC BD 2. _________________________________________________ </p><p>3. 1 &amp; 2 are right s. 3. _________________________________________________ </p><p>4. 1 2 4. _________________________________________________ </p><p>5. BD BD 5. _________________________________________________ </p><p>6. ADB CDB 6. _________________________________________________ </p><p>#2 </p><p>Given: AC BD </p><p> BD bisects ADC </p><p>Prove: AB CB </p><p>1. AC BD 1. _________________________________________________ </p><p>2. 1 &amp; 2 are right s 2. _________________________________________________ </p><p>3. 1 2 3. _________________________________________________ </p><p>4. BD BD 4. _________________________________________________ </p><p>5. BD bisects ADC 5. _________________________________________________ </p><p>6. 3 4 6. _________________________________________________ </p><p>7. ADB CDB 7. _________________________________________________ </p><p>8. AB CB 8. _________________________________________________ </p><p>B </p><p>3 4 </p><p>1 2 </p><p>D </p><p>A C </p><p>D </p><p>B </p><p>3 4 </p><p>1 2 A C </p></li><li><p>14 </p><p>Congruent Triangles Proofs </p><p>1. Given: SP ; O is the midpoint of PS </p><p> Prove: O is the midpoint of RQ </p><p>2. Given: ABCD ; D is the midpoint of AB </p><p> Prove: CBCA </p><p>3. Given: KRSNNRSK //;// </p><p> Prove: KRSNNRSK ; </p><p>4. Given: MEADMEAD ;// </p><p> M is the midpoint AB </p><p> Prove: EBDM // </p><p>5. BONUS Given: DACDABACAB ; </p><p> Prove: BCD is isosceles </p><p>7. BONUS Given: PRMRQRPQRM ; </p><p> Prove: PQMQ </p><p>A B </p><p>C </p><p>D </p><p>S </p><p>K </p><p>N </p><p>R </p><p>1 </p><p>2 3 </p><p>4 </p><p>A M B </p><p>E D </p><p>A </p><p>C B </p><p>D </p><p>Q </p><p>R </p><p>P </p><p>M </p><p>P </p><p>O </p><p>R S </p><p>Q </p></li><li><p>15 </p><p>8. Given: </p><p>DCDE</p><p>BDAD</p><p>BCAE</p><p> Prove: ADCEDB </p><p>9. Given: MKAB </p><p> B is the midpoint of MK Prove: yx </p><p>10. Given: 21 </p><p> FMCD </p><p> Prove: CD bisects MCF </p><p>11. Given: QVPV</p><p>QSPS</p><p>//</p><p>// </p><p> Prove: yx </p><p>12. Given: </p><p>BDAE</p><p>CDCE</p><p>BCAC</p><p> Prove: 21 </p><p>13. Given: </p><p>ABDB</p><p>BEBC</p><p>BEDB</p><p>BCAB</p><p> Prove: AD </p><p>A B </p><p>C </p><p>D </p><p>E A </p><p>B M K </p><p>x y </p><p>C D </p><p>M </p><p>F </p><p>1 </p><p>2 S </p><p>Q V P </p><p>x Y </p><p>C </p><p>A D E B </p><p>1 2 </p><p>E </p><p>A </p><p>B </p><p>D </p><p>C </p></li><li><p>16 </p><p>14. Given: D and C are supplementary </p><p> B and C are supplementary </p><p> BEDFABAD , </p><p> Prove: yx </p><p>15. Given: RSTSSKSL , </p><p> Prove: LK </p><p>16. Given: RDDABRBA , </p><p> Prove: RAXDBX </p><p>17. Given: </p><p>ZOYO</p><p>ZXZOYXYO</p><p> , </p><p> Prove: ZXYX </p><p>18. Given: GFBCEFCD</p><p>CFGECFBD</p><p>,</p><p>, </p><p> Prove: ACF is isosceles </p><p>19. Given: BCAB </p><p> BD is a median of ABC </p><p> Prove: CBDABD </p><p>20. Given: PR bisects QPS </p><p> PR is an altitude of QPS </p><p> Prove: PQS is isosceles </p><p>A B </p><p>E </p><p>C F D </p><p>x </p><p>y </p><p>S </p><p>R </p><p>K </p><p>T </p><p>L </p><p>B D </p><p>A </p><p>X </p><p>R </p><p>Y </p><p>O </p><p>Z </p><p>X A </p><p>B </p><p>C D E </p><p>F </p><p>G </p><p>B </p><p>C </p><p>D </p><p>A </p><p>P </p><p>Q </p><p>R </p><p>S </p></li></ul>


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