# Name Period 11/2 11/13

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1 Name Period 11/2 11/13 Vocabulary erms: ongruent orresponding Parts ongruency statement Included angle Included side GOMY UNI 6 ONGUN INGL HL Non-included side Hypotenuse Leg 11/5 and 11/12 eview 11/6,, HL 11/13 est 11/7-8 ongruent riangles and Logic 11/2 ongruent Polygons 11/9 P Friday, 11/2 hapter 4 ection 3: ongruent riangles I can match the corresponding parts of congruent figures given a picture or a congruency statement. I can prove polygons congruent using the definition of congruent polygons. IGNMN: Pg. 234 (#2-11, 13-16, 19, 21-22, 28-31) ompleted: Monday, 11/5 hapter 4 ection 4: riangle ongruence: and I can determine if 2 triangles are congruent using or. IGNMN: riangle ongruence W -#2, 4, 8, 9, 13, 15, 16, 19 ompleted: uesday, 11/6 hapter 4 ection 5: riangle ongruence:,, and HL I can determine if 2 triangles are congruent using,, or HL. IGNMN: riangle ongruence W - Finish ompleted: Wednesday or hursday, 11/7-8 hapter 4 ection 4 and 5: riangle ongruence: and N,, and HL I can determine if 2 triangles are congruent using,,,, or HL. I can determine the missing piece of information needed to prove triangles congruent I can complete a fill-in-the-blank proof. I can use triangle congruence and logic to solve problems. IGNMN: riangle ongruence and Logic Worksheet ompleted: Friday, 11/9 hapter 4 ection 6: P I can use P to solve different types of problems. I can use P in geometric proofs IGNMN: P Worksheet ompleted:

2 Monday, 11/12 IGNMN: eview for est uesday, 11/13 Unit 6 est: ongruent riangles eview ay est ay ompleted: Grade: If you miss the review day, you are still expected to take the test on the test day. For more help FO the test: 1. Use the indicated chapters in your book 2. Use the book online (it has videos and a homework help section) 3. Use Google to find more resources 4. ome to tutoring (with assignment)

3 ONGUN Polygons xamples I. Name the congruent triangles. 2. FOX 1. LIN I O O F L N X X II. Name the congruent triangle and the congruent parts.. 3. FGH FI FG G GH H FH Use the congruency statement to fill in the corresponding congruent parts. 4. FI HGI F FI FI FI I

4 xample 3: Proving riangles ongruent Given: YWX and YWZ are right angles. YW bisects XYZ. W is the midpoint of XZ. XY YZ. Prove: XYW ZYW heck It Out! xample 3 Given: bisects. bisects., Prove:

5 heck It Out! xample 4 Use the diagram to prove the following. Given: MK bisects JL. JL bisects MK. JK ML. JK ML. Prove: JKN LMN

6

7 Name Period riangle ongruence 1. List the five ways to prove that triangles are congruent. For each pair of triangles, tell which of the above postulates make the triangles congruent. 2. F 3. F 4. F 5. F M M M

8 Q P F HIJ QOP P P 8. P Q F H J I P Q O P

9 Name Period riangle ongruence and Logic Worksheet I. For each pair of triangles, tell: (a) re they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent a. a. a. b. b. b. c. c. c M I L I O W H L V a. a. a. b. b. b. c. c. c L U H P W G M a. a. a. b. b. b. c. c. c.

10 II. Using the given postulate, tell which parts of the pair of triangles should be shown congruent F F HL 15. P P Q Q III. Multiple hoice 16. Which set of coordinates represents the vertices of a triangle congruent to? (Hint: Find the y lengths of the sides of ). (3, 4) (3, 0) (0, 0) 6. (3, 3) (0, 4) (0, 0). (3, 1) (3, 3) (4, 6) 4. (3, 0) (4, 4) (0, 6) 2 x Given and F. Which of the following pairs of corresponding parts would correctly prove the triangles congruent by?.,,. F,,., F,.,, F

11 For 18 19: Fill in the blank with the correct statement or reason to complete the proofs. 18. GIVN: Z bisects ; 3 4 POV: Z Z Z 1. Z bisects MN ON 2. efinition of a segment bisector 3. Given 4. Z Z 5. Z Z. eflexive Property. Given Z Z. 19. GIVN: Q ; is the midpoint of Q. POV: PQ P MN 1. Q 2. Given 3. Q 4. Vertical ngle heorem 5. PQ. PQ. efinition of midpoint. Q ON. Given. is the midpoint of Q Given: is the midpoint of, Which of the following statements must be true?

12 22. In the figure below, F and F Which additional information would be enough to prove F? F raw a counterexample for the following statement. If the 3 angles in one triangle are congruent to the corresponding angles in another triangle, then the 2 triangles are congruent. P Notes

13 I. P stands for. his means that once you have proven the 2 triangles, you know that all the parts are also. xamples: 1) Find JK 2) 3) dditional xamples from worksheet: # 3, 5, and 16

14 P Worksheet I. olve for the variable. 1. OG. Find h. 2. IF HGF. Find a. F O G 15 h 38 a I H G 3. PQ MN. Find x. 4.. Find y. Q (3y) 21 P x M 35 o N II. et up an equation and then solve for the variable. 5. OG. Find x. 6. IF HGF. Find a. F O G (8x-6) (3x+9) (5a) o (2a+3) o I H G 7.. Find x. 8.. Find y. 7 y (2x+17) o (4x-35) o 3y + 20

15 III. For which value(s) of x are the triangles congruent? 9. x = 10. x = 5x - 8 F 3x + 2 5x x = 12. x = m 3 = 3x m 4 = 7x x + 8 7x x = 14. x = 19 9x - 8 m = (15x + 3) m = (10x + 18) 15. x = 16. x = (2x + 4) 2 W x 2 + 2x x Z 1 (4x 6)

16 IV. Proofs 17. GIVN: N is the midpoint of X NY NX Y POV: X Y X N Y MN 1. N is the midpoint of 2. efinition of a midpoint 3. X NY 4. Given 5. XN NY 6. P ON 18. GIVN: V V POV: V V MN ON 1. Given eflexive V 19. GIVN: V bisects VO V bisects O POV: O O ON MN 1. V bisects VO 2. efinition of ngle isector 3. Given V V O V

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