Name: Period: Geometry Honors Unit 3: Congruency Homework Section 3.1: Congruent Figures Can you conclude that the triangles are congruent? Justify your answer. 1. ΔGHJ and ΔIHJ 2. ΔQRS and ΔTVS 3. ΔFGH and ΔJKH 4. ΔABC and ΔFGH ABCD FGHJ. Find the measures of the given angles or lengths of the given sides. (Draw a picture to help!) 5. m B = 3y, m G = y + 50 6. CD = 2x + 3 and HJ = 3x + 2 7. m C = 5z + 20, m H = 6z + 10 Draw two congruent triangles and label the vertices given that CAT JSD. List each of the following. 8. Three pairs of congruent sides 9. Three pairs of congruent angles Draw a triangle. Label the vertices A, B, and C. 10. What angle is between BC and AC? 11. What sides include B? 12. What angles include AB? 13. What side is included between A and B? 14. Given: BD is the angle bisector of ABC. 15. Given: AD and BE bisect each other. BD is the perpendicular bisector of AC. AB DE and A D. PROVE: ADB CDB PROVE: ACB DCE (Hint: 9 steps!) (Hint: 8 steps!) REVIEW: Find the value of the variable and the measures of all of the angles. 1. 2. 3.
Section 3.2: Triangle Congruency by SSS and SAS Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. IF YOU DO NOT COMPLETE THE PROOFS YOU WILL RECEIVE A 0 ON THIS HOMEWORK ASSIGNMENT!!! 14. Given: BC DC, AC EC PROVE: ABC EDC 15. Given: WX YZ, WX YZ PROVE: WXZ YZX 16. Given: RX SX, QX TX PROVE: QXR TXS 17. Given: BD is the perpendicular bisector of AC PROVE: BAD BCD 18. Given: AC bisects BD, AB AD Prove: ABC ADC REVIEW: Identify which type of angle pair is shown in the diagram and tell if they are congruent or supplementary. 1. 2. 3. 4. 5.
Section 3.3: Triangle Congruency by ASA and AAS Would you use ASA or AAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent, write not enough information. 1. 2. 3. 4. 5. 6. 7. 8. 9. Name the two triangles that are congruent by ASA. 10. 11. 12. IF YOU DO NOT COMPLETE THE PROOFS YOU WILL RECEIVE A 0 ON THIS HOMEWORK ASSIGNMENT!!! 13. Given: BD AC, BD bisects ABC 14. Given: KJ MN, KJL MNL 15. Given: BD is the angle bisector PROVE: ABD CBD PROVE: JKL NML of ABC and ADC PROVE: ABD CBD REVIEW: Sketch a diagram of the description. 1. Plane R and line k intersecting plane R at a right angle 2. AB in plane R bisected by point C, with point D also on AB 3. AB in plane R with ray CD such that point D is on AB 4. Planes R and S with line XY intersecting each plane
Section 3.4: Congruency in Right Triangles What additional information would prove each pair of triangle congruent by HL? 1. 2. 3. 4. 5. 6. For what values of or x and y are the triangles congruent by HL? 7. 8. 9. 10. IF YOU DO NOT COMPLETE THE PROOFS YOU WILL RECEIVE A 0 ON THIS HOMEWORK ASSIGNMENT!!! 11. Given: RT SU, RU RS 12. Given: AD bisects EB, AB DE, PROVE: RUT RST ACB and ECD are right angles PROVE: ACB DCE REVIEW: Find the value of the variable that makes the lines parallel. 1. 2. 3.
Section 3.5: Corresponding Parts of Congruent Triangles Tell how you would prove the triangles congruent. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 11. GIVEN: ZW XY, YXW and 12. GIVEN: LP LO, PM ON 13. GIVEN: ABC DCB, CBD BCA ZWX are right s Complete each proof. 14. Given: YA BA, B Y 15. Given: BD AB, BD DE, BC DC 16. Given: FJ GH, JFH GHF PROVE: AZ AC PROVE: A E PROVE: FG JH REVIEW: AB = -7x + 13 BC = 9 3x AC = 42 A B C 1. Solve for x. 2. Find AB. 3. Find BC.
Unit 3 Review Which theorem could you use to prove the two triangles congruent? 1. 2. 3. 4. 5. 6. 7. 8. WXYZ PQRS. Find the measure of the angle or the length of the side. 9. P 10. QR 11. WX 12. Z 13. X Write a congruence statement for each pair of triangles. How do you know they are congruent? 14. 15. 16. 17. Complete each proof. 18. Given: AE CB, AB CD, and B is the midpoint of ED Prove: AEB CBD 19. Given: AB BE, DE BE, AC DC, and BAC EDC Prove: ABC DEC 20. Given: GK ML, GKM LMK Prove: GKM LMK 21. Given: S R and XT bisects SXR Prove: SXT RXT 22. Given: H is the midpoint of MK and QD Prove: QMH DKH 23. Given: SQ bisects PSR and P R Prove : SQP SQR