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Name: ______________________________ Date: ________ Block: _____ Geometry Chapter 4 Review Find the value of x. Then classify the triangle by its angles. 1. 2. 3. x = __________ x = __________ x = __________ classify: _______ classify: _________ (x + 12)° classify: _________ 4. x = _________ classify: _________ Complete the congruence statement for the figures. 5. ABCD ≅ ______ State the congruence that is needed to prove ∆ABC ≅ ∆DEF using the given postulate or theorem. 6. Given: BC EF ; Use the Hypotenuse-Leg Congruence Theorem 7. Given: AB DE , AC DF ; Use the SSS Congruence Postulate 8. Given: ∠A ≅ ∠D, ∠B ≅ ∠E; Use the AAS Congruence Theorem 9. Given: ∠A ≅ ∠D, ∠C ≅ ∠F; Use the ASA Congruence Postulate Decide whether the triangles can be proven congruent by the given postulate or theorem. 10. ∆TWX ≅ ∆YWX by SSS yes / no Find the value of x. 11. 12. 5x - 2 x = __________________ 3x + 8 x = ___________________ Use the diagram to find the measure. 13. m∠ WYX = _____ 14. WX = _____ Is it possible to prove ∆ABC ≅ ∆DEF using the given information? If so, state the postulate or theorem you would use. 15. AB DE , AC DF , BC EF 16. ∠A ≅ ∠D, AB DE , BC EF 17. ∠A ≅ ∠D, ∠C ≅ ∠F, ∠B ≅ ∠E 18. ∠A ≅ ∠D, ∠C ≅ ∠F, BC EF Part 2 of Chapter 4 Review #1-3. Classify the following triangles by the number of sides. 1) ________________ 2) _________________ 3) _________________ #4-6. Classify the following triangles by their angles. 4) ________________ 5) _________________ 6) _________________ #7-8. Given: AB BC 7) Solve for x. equilateral? 8) Is the triangle 9) How many obtuse angles can an isosceles triangle have? __________ 10) In ABC, AB BC . Which term does not describe the triangle? a) b) c) d) acute isosceles equilateral obtuse 11) In a right triangle, the side across from the right angle is called the ___________________. 12) ABC DEF. Also AB EF . What type of triangle is ABC? _______________________ (Hint: Draw both triangles!) #13-15. Find the measures of the numbered angles. 13) m1 = ___________ 14) m2 = ___________ 15) m3 = ___________ 16) Find the measure of BCD. mBCD = __________ #17-19. Find the measures of A, B, and C. 17) mA = ________ 18) mB = ________ 19) mC = ________ 20) Refer to the figure on the right. mA= ________. 21) The measure of B is_________. #22-24. What are the values of x, y, and z? 22) x = _________ 23) y = _________ 24) z = _________ #25-27. In ∆ABC, A C and B is a right angle. Find the measure of each angle. 25) mA = __________ 26) mB = __________ 27) mC = __________ #28-29. Find the value of y. 28) y = _____________ 29) y = ______________ #30-32. In the diagram, ∆TJM ∆PHS. Complete the statements below. 30) P ___________ 31) mM ___________ 32) ∆HPS ___________ 33) State two methods (i.e. SSS, SAS, ASA, AAS, or HL) that can be used to conclude that AOB COD. Method 1: __________ Method 2: __________ 34) Given AB DE and B E, what would you use to prove that ABC DEC (SSS, SAS, ASA, AAS, or HL)? Answer: ___________ 35) Given BAC DAC and B D, what would you use to prove that ABC ADC (SSS, SAS, ASA, AAS, or HL)? Answer: ______________ 36) ABD CBD. Name the theorem or postulate (ex. SSS, SAS, ASA, AAS, or HL) that justifies the congruence. Answer: ______________ #37-40. Tell which method(s) you can use to prove that the triangles are congruent. If no method can be used, write “none”. 37. Answer: ___________ 38. Answer: ___________ 39. Answer: ___________ 40. Answer: ___________