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Name _________________________________________ Period ____ 10/24 – 11/3 Pre-AP UNIT #6: TRIANGLE CONGRUENCE I can define, identify and illustrate the following terms congruent polygons obtuse triangle equilateral triangle exterior angle equiangular triangle scalene triangle right triangle acute triangle interior angle auxiliary lines isosceles triangle SSS SAS AAS HL ASA Dates, assignments, and quizzes subject to change without advance notice Monday 24 Classifying and Angle Relationships 31 CPCTC Tuesday 25 Isosceles, Equilaterals, and Congruent Polygons 1 Review Block Day 26/27 Congruent Triangles (with basic proofs) Friday 28 Proofs QUIZ 2/3 TEST Monday, 10/24 Classifying Triangles (4-1) and Angle Relationships in Triangles (4-2) Check Point Grade: 2) I can classify triangles by sides and angles 3) I can use triangle classifications to find angle measures and side lengths. 4) I can use triangle sum theorem to solve missing angles of a triangle 5) I can use exterior angle theorem to find missing angles of a triangle Grade: ASSIGNMENT: pg 219 #13-19 odd, 24-34 even 35-37 all (13 Test /41 = % /6 /12 problems) pg. 223 #17-21, 23, 29-34, 44, 45 (14 problems) Tuesday, 10/25 Congruent Polygons (4-3) and Triangle Properties (4-8) Check Point Grade: 6) I can use the properties of equilateral triangles to find missing side lengths and angles Test /17 = % /9 7) I can write a congruency statement representing two congruent polygons 8) I can identify congruent parts of a polygon, given a congruency statement 9) I can find the side lengths and angle measures using properties of congruent polygons 10) I can use the properties of isosceles triangles to find missing side lengths and angles ASSIGNMENT: pg. 277 #13-19 odd, 22-26, 28, 29, 33, 34 (13 Grade: problems) pg. 235 #19, 23-25, 30-36 (11 problems) /8 Wednesday and Thursday, 10/26-27 Determine if Triangles are Congruent (4-4 and 4-5) Check Point Draw and describe the five ways to Grade: show that two triangles are congruent. 11) I can name the five ways to prove triangles are congruent 12) I can determine whether triangles are congruent 13) I can prove triangles are congruent using SSS, ASA, AAS, SAS, HL. 14) I can mark pieces of a triangle congruent given how they are to be proved congruent. ASSIGNMENT: Triangle Congruence Worksheet Grade: Test /54 = % Tested below /36 /8 /10 Friday, 10/28 Proofs Check Point Grade: 15) I can write a two-column proof to show that two triangles are congruent. ASSIGNMENT: Proofs Worksheet Test /41 = % /6 Grade: Monday, 10/31 Triangle Proofs with CPCTC Check Point How many corresponding parts should be listed in your Grade: proof before you can conclude triangles are congruent? 15) I can write a two-column proof to show that two triangles are congruent. ASSIGNMENT: Triangle Proofs Worksheet Grade: Test /12 = % /12 Tuesday 11/1 Review I can assess my knowledge and prepare for the test. ASSIGNMENT: Review Worksheet Grade: Wednesday and Thursday, 11/2-3 Test 7 –Triangle Congruence I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material. ASSIGNMENT: Test #7 Test Grade: Name __________________________ Period ______ Triangle Congruence GH I. For each pair of triangles, tell which postulate can be used to prove the triangles congruent. 1. ∆AEB ≅ ∆DEC ______________ 2. ∆CDE ≅ ∆ABF ______________ A D E C F C B E A B D 3. ∆DEA ≅ ∆BEC A ______________ 4. ∆AGE ≅ ∆CDF ______________ B E D C 5. ∆RTS ≅ ∆CBA ______________ 6. ∆ABC ≅ ∆ADC ______________ B T S C A C R A 7. ∆BAP ≅ ∆BCP Given: BD bisects B ______________ ABC D 8. ∆SAT ≅ ∆SAR ______________ A R S A B D P T C II. For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent. 1. D 2. C 3. Given: T is the midpoint of WR O A E T E L A E R W V B a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ 4. 5. Given: IH Bisects WIS 6. I W H S L U G E a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ 7. 8. 9. H P A T M a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ 10. Given: I is the midpoint of ME and SL M 11. 12. C F L I S E B A D E a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ III. Using the given postulate, tell which parts of the pair of triangles should be shown congruent. 1. SAS 2. ASA 3. SSS C A E D B F F B A B A E D C C D _______ ≅ ________ 4. AAS ________ ≅ ________ 5. HL _______ ≅ _______ 6. ASA P P D S C T R A Q _______ ≅ ________ R S Q ________ ≅ ________ _______ ≅ _______ B IV. For which value(s) of x are the triangles congruent? 1. x = _______________ 2. x = _______________ D D 5x - 8 F E B A 5x° 92° 3x + 2 E C A B 3. x = _______________ A C 4. x = _______________ A B m ∠3 = x2 m ∠4 = 7x - 10 7x - 4 4x + 8 1 3 E 2 4 C D C 5. x = _______________ A 6. x = _______________ C D 2 x + 3x B D C 9x - 8 A B m ∠ CDB = (15x + 3)° 7. x = _______________ C W (2x + 4)° A m ∠ ABD = (10x + 18)° 8. x = _______________ D 1 B R 2 Z x2 + 2x x2 + 24 (4x – 6)° B R S T Name: Period: GH Triangle Proofs Worksheet For each problem below, write a two-column proof on a separate piece of paper. I. Proving Triangles Congruent: 1. 5. 2. 3. 6. 4. II. Using CPCTC 7. 10. 1 8. 9. 2 11. Review: Triangles and Triangle Congruence You will need a separate piece of paper to show all your work. This review is not comprehensive; always be sure to go back through your old homework and quizzes. C I can write a congruency statement representing two congruent polygons O G 1. Write a congruency statement for the two triangles at right. R A E I can identify congruent parts of a polygon, given a congruency statement 2. List ALL of the congruent parts if EFG ≅ HGF I can use algebra to find the side lengths and angle measures of congruent polygons 3. WXY ≅ZYX . Find p. X Y 2 2p V 20 (7p+13 W Z 4. ADC ≅CBA. Find x. D C (2x 2 + 7)° 1 2 (x 2 – 8x)° A B I can name the five ways to prove triangles are congruent 5. Name the 5 ways to prove triangles congruent. I can prove triangles are congruent For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent. B 6. 8. Given: I is the midpoint of ME and SL A C M L I D 7. S A E T W R E I can mark pieces of a triangle congruent given how they are to be proved congruent P 9. What information is 10. What information is missing to use missing to use HL? SAS? C D R S Q A B I can use the exterior angle theorem and the triangle sum theorem to solve problems. 12. The measures of the angles of a triangle 11. Solve for x and find the measure of the following angles. G are in the ratio of 1:4:7. What are the measures of the angles? OGE = ______ GEO = ______ EOM = ______ (x +16)o (5x + 18)o E O (3x + 100)o M I can use the properties of isosceles and equilateral triangles to solve problems. 13. Draw and correctly mark the sides and angles of an equilateral, isosceles, and a scalene triangle. 14. Solve for x. (-5x + 41) (3x – 15) 15. The vertex angle of an isosceles triangle measures (6t – 9)° and one of its base angles measures (4t)°. Find t. I can write a two-column proof over congruent triangles 16. 17. Complete and review ALL proofs on the proofs worksheet.