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Homework 4-1 𝑪𝑨𝑻 𝑱𝑺𝑫. List each of the following. 1. three pairs of congruent sides 𝑪𝑨 ≅ 𝑱𝑺 𝑨𝑻 ≅ 𝑺𝑫 𝑪𝑻 ≅ 𝑱𝑫 2. three pairs of congruent angles ∠𝑪 ≅ ∠𝑱 ∠𝑨 ≅ ∠𝑺 ∠𝑻 ≅ ∠𝑫 Mrs. Rivas Homework Mrs. Rivas Algebra Find the values of the variables. 3. 𝟓𝒙 𝟕𝟒 𝟓𝒙 + 𝟕𝟒 + 𝟑𝒙 + 𝟐 = 𝟏𝟖𝟎 𝟖𝒙 + 𝟕𝟔 = 𝟏𝟖𝟎 𝟖𝒙 = 𝟏𝟎𝟒 𝒙 = 𝟏𝟑 Homework Algebra Find the values of the variables. 4. 𝟐𝒙 = 𝟏𝟎 𝒙=𝟓 Mrs. Rivas Homework Mrs. Rivas Algebra ABCD FGHJ. Find the measures of the given angles or lengths of the given sides. 5. 𝑚𝐵 = 3𝑦, 𝑚𝐺 = 𝑦 + 50 A B D C 𝟑𝒚 = 𝒚 + 𝟓𝟎 𝟐𝒚 = 𝟓𝟎 𝒚 = 𝟐𝟓 F G 𝒎𝑩 = 𝟑𝒚 𝒎𝑩 = 𝟑(𝟐𝟓) 𝒎𝑩 = 𝟕𝟓 𝒎𝑮 = 𝒚 + 𝟓𝟎 𝒎𝑮 = 𝟐𝟓 + 𝟓𝟎 J H 𝒎𝑮 = 𝟕𝟓 Homework Mrs. Rivas Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths of the given sides. 6. 𝐶𝐷 = 2𝑥 + 3; 𝐻𝐽 = 3𝑥 + 2 A D B C F G J H 𝟐𝒙 + 𝟑 = 𝟑𝒙 + 𝟐 𝟑=𝒙+𝟐 𝟏=𝒙 𝑪𝑫 = 𝟐𝒙 + 𝟑 𝑪𝑫 = 𝟐(𝟏) + 𝟑 𝑪𝑫 = 𝟓 𝑯𝑱 = 𝟑𝒙 + 𝟐 𝑯𝑱 = 𝟑(𝟏) + 𝟐 𝑯𝑱 = 𝟓 Homework Mrs. Rivas Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths of the given sides. 7. 𝑚𝐶 = 5𝑧 + 20, 𝑚𝐻 = 6𝑧 + 10 A B D C 𝟐𝟎 = 𝒛 + 𝟏𝟎 𝒎𝑪 = 𝟓𝒛 + 𝟐𝟎 𝒎𝑪 = 𝟓 𝟏𝟎 + 𝟐𝟎 𝟏𝟎 = 𝒛 𝒎𝑪 = 𝟕𝟎 𝟓𝒛 + 𝟐𝟎 = 𝟔𝒛 + 𝟏𝟎 F G 𝒎𝑯 = 𝟓𝒛 + 𝟐𝟎 𝒎𝑪 = 𝟓 𝟏𝟎 + 𝟐𝟎 J H 𝒎𝑪 = 𝟕𝟎 Homework Mrs. Rivas Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths of the given sides. 8. 𝐴𝐷 = 5𝑏 + 4; 𝐹𝐽 = 3𝑏 + 8 A D B C F G J H 𝟓𝒃 + 𝟒 = 𝟑𝒃 + 𝟖 𝟐𝒃 + 𝟒 = 𝟖 𝟐𝒃 = 𝟒 𝒃=𝟐 𝑨𝑫 = 𝟓𝒃 + 𝟒 𝑨𝑫 = 𝟓(𝟐) + 𝟒 𝑨𝑫 = 𝟏𝟒 𝑭𝑱 = 𝟑𝒃 + 𝟖 𝑭𝑱 = 𝟑(𝟐) + 𝟖 𝑭𝑱 = 𝟏𝟒 Homework Mrs. Rivas 4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below. 9. What angle is included between 𝐺𝑀 and 𝑀𝑇? G M ∠𝑴 T Homework Mrs. Rivas 4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below. 10. Which sides include ∠𝑇? G 𝑻𝑮 𝒂𝒏𝒅 𝑻𝑴 M T Homework Mrs. Rivas 4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below. 11. What angle is included between 𝐺𝑇 and 𝑀𝐺 ? G M ∠𝑮 T Mrs. Rivas Homework 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. Explain your answer. 13. 12. Not enough information; two pairs of corresponding sides are congruent, but the congruent angle is not included. SAS; two pairs of corresponding sides and their included angle are congruent. Homework Mrs. Rivas 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. Explain your answer. 15. 14. SSS; three pairs of corresponding sides are congruent. Not enough information; two pairs of corresponding sides are congruent, but the congruent angle is not the included angle. Homework Mrs. Rivas 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. Explain your answer. 16. SSS; three corresponding sides are congruent 17. SAS; two pairs of corresponding sides and their included right angle are congruent. Homework Mrs. Rivas 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. Explain your answer. 18. Not enough information; one pair of corresponding sides and corresponding angles are congruent, but the other pair of corresponding sides that form the included angle must also be congruent. 19. SAS; two pairs of corresponding sides and their included vertical angles are congruent. Homework Mrs. Rivas 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. Explain your answer. 20. SSS or SAS; three pairs of corresponding sides are congruent, or, two pairs of corresponding sides and their included vertical angles are congruent. Mrs. Rivas Homework 4-3 Name two triangles that are congruent by ASA. 21. 22. ∆𝑯𝑰𝑱 ≅ ∆𝑴𝑳𝑲 ∆𝑹𝑺𝑻 ≅ ∆𝑿𝒀𝒁 Homework Mrs. Rivas 23. Developing Proof Complete the proof by filling in the blanks. Given: 𝐻𝐼𝐽 ≅ ∠𝐾𝐼𝐽, and 𝐼𝐽𝐻 ≅ ∠𝐼𝐽𝐾 Prove: 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽 Proof: 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽 and 𝐼𝐽𝐻 ≅ 𝐼𝐽𝐾 are given. 𝑪𝒐𝒏𝒈𝒓𝒖𝒆𝒏𝒕 𝑷𝒓𝒐𝒑𝒆𝒓𝒕𝒚 _____. 𝐼𝐽 ≅ 𝐼𝐽 by 𝑹𝒆𝒇𝒍𝒆𝒙𝒊𝒗𝒆 𝑨𝑺𝑨 So, 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽 by _____. Homework 24. Given: 𝐿𝑂𝑀 ≅ 𝑁𝑃𝑀,𝐿𝑀 ≅ 𝑁𝑀 Prove: 𝐿𝑂𝑀 ≅ 𝑁𝑃𝑀 Proof: ∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 and 𝑳𝑴 ≅ 𝑵𝑴 are given. ∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 because vertical angles are ≅. So, ∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 by AAS. Mrs. Rivas