Given: a // b & s // t Prove: 4 @ 13 1 9 10 2 a 3 4 11 12 5 6 13 14 b 7 16 8 15 t s
Congruent Figures - Figures that have the same size and shape. Hypothesize with your partner…what do you think is true, specifically, about these two congruent triangles . C D ABC @ D DEF F B A E D
1. Identify the corresponding parts of congruent figures. 2.Formally prove triangles are congruent using postulates and theorems. 3.Deduce information about segments and angles after proving that two triangles are congruent. 4.Apply the following vocabulary terms – median, altitude, perpendicular bisector. 5.Refine proof construction skills.
D ABC @ D DEF Observations - A @ D AB @ DE B @ E EF BC @ DF AC @ C @ F C F 90° 90° 3in 4in 3in 4in D E 53° 37° 53° 37° B A 5in 5in
Conclusion Corresponding Parts of Congruent Triangles are Congruent.
D Practice - CPCTC Given : D CAT @ D DOG CA @ DO C @ D CT @ A @ DG O C AT @ OG T @ G O G Two triangles are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are A congruent. T
Practice - CPCTC Given : D PIG @ D COW Make sure PG @ CW P @ C the letters PI @ I @ CO O match up!! IG @ OW G @ W How else could you name the congruent triangles? D PIG @ D COW D GIP @ D WOC D PIG @ D WOC D IPG @ D OCW D GIP @ D COW D GPI @ D WCO D IPG @ D WCO D PGI @ D CWO D IGP @ D OWC
Practice - CPCTC N AN @ GB A @ G A AT @ GU N @ B NT @ BU T @ U T U G D BUG @ D NTA B
Partner Practice p. 119 # 1-11 #11 – Write a Proof!
D FIN @ D WEB p. 119 # 1-4 1.Name the three pairs of corresponding sides. FN @ FI @ IN @ WE EB WB 2. Name the three pairs of corresponding angles. W F @ I @ N @ E B 3. Is it correct to say D NIF @ D BEW? Yes 4. Is it correct to say D INF @ D EWB? No
p. 119 # 5 - 9 D C O A B 9. Can you deduce that 5. D ABO @ D CDO O is the midpoint of any C 6. A @ segment? 7. AO @ CO Yes. O is the midpoint of AC and DB because 8. BO @ DO AO = OC and DO = OB.
p. 119 # 10 D C O A B 10. Explain how you can deduce that DC // AB. A @ C If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
11. Suppose you know that DB ^ DC. Explain how you can deduce that DB ^ BA. D C O A B 1. Given 1. DB ^ DC; D ABO @ D CDO 2. Definition of perpendicular lines. 2. D is a right angle 3. m D = 90 3. Definition of a Right Angle 4. m D = m B 4. CPCTC 5. m B = 90 5. Substitution 6. B is a right angle 6. Definition of a Right Angle 7. DB ^ BA 7. Definition of perpendicular lines.
Something to think about… What do you think might be true about other congruent polygons? Such as two congruent pentagons. G B A F H C J K D E
HW p. 120 WE #1-8, 10, 11, 20, 21, 23 Draw all diagrams.
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