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Geometry Congruent Triangles CHAPTER 4 REVIEW PERIOD_____ NAME _________________ DATE______ Classify the triangle by its sides (equilateral, isosceles, scalene) and by its angles (acute, right, obtuse, equiangular) . _________________________1. 1) _________________________2. 2) _________________________3. _________________________4. 3) 4) _________________________5. _________________________6. 5) Find the measure of the numbered angles. 7. m1 _______ 8. m2 _______ 9. m3 _______ 10. m4 _______ 11. m5 _______ 12. m6 _______ 6) Find x and y 13. x=________ y=_______ 13) 14. 14) x=________ y=_______ 15. x=________ 15) y=_______ Write an equation to find the value of the variable, find x, and find the measure of the indicated angle. Justify the equation. 16. Equation____________________ x=________ mBCA ________ 17) 17. Equation____________________ x=________ mBCD ________ 18. Equation____________________ 18) x=________ 19. Equation____________________ 19) x=________ 20. Equation____________________ x=________ 20) 16) In the diagram, ABC DEF . Complete the statement 21. BC _____ 22. A _____ 23. x _____ 24. y _____ 25. mB _____ 26. mC _____ 27. BCA ________ 28. CAB ________ Decide whether you can deduce by the SSS, SAS, ASA, AAS, or HL that the triangles are congruent. If so, complete the congruence statement and name the postulate used. If not, write no congruence can be deduced. Remember to mark any other congruent parts (vertical angle, reflexive, alternate interior angles, etc) 29. 30. Method__________ Method__________ WLF ________ RST ________ 31. 32. Method__________ Method__________ BCD ________ GHK ________ 33. 34. Method__________ Method__________ GNL ________ BCD ________ State the third congruence that is needed to prove GHI IJG using the indicated postulate or theorem. Label congruent parts. Remember to mark any other congruent parts (vertical angle, reflexive, alternate interior angles, etc) 35. Using the HL Congruence Postulate H is a right angle J is a right angle _______ _______ 36. Using the SAS Congruence Theorem GH JI _______ _______ 37. Using the SSS Congruence Theorem GH JI _______ _______ State the third congruence that is needed to prove CBE DBA using the indicated postulate or theorem. Label congruent parts. Remember to mark any other congruent parts (vertical angle, reflexive, alternate interior angles, etc) 38. Using the ASA Congruence Postulate A E _______ _______ 39. Using the AAS Congruence Postulate A E _______ _______ Complete the following two-column proofs. Redraw triangles and label any congruent parts. 40. GIVEN: VW UW X Z XWV ZWU PROVE: Statements Reasons 1. X Z 1. 2. 2. Given 3. W W 3._________________________________ 4. ________________________ 4._________________________________ 41. GIVEN: JKL is a right angle LJ KM KLM is a right angle PROVE: J M Statements Reasons 1. KL KL 1._________________________________ 2. 2. Given 3. JKL is a right angle 3._________________________________ KLM is a right angle 4. JKL is a right triangle KLM is a right triangle 5. 6. ________________________ 4._________________________________ 5. HL Postulate 6. _________________________________ 42. Find the measure of the indicated angle or length: MKL ___________________ ST ___________________ 43. Find the values of x and y. x ___________________ x ___________________ y ___________________ y ___________________ 44. Write the equation of the new line: a) Parallel to y 2 x 10 and through point P(-5, -4) 1 b) Perpendicular to y x 6 and through point Q(4, 5) 3 45. The coordinates for points A and B are, A(-2, 5) and B(8, -6). Find the distance and midpoint. AB ___________________ M ___________________