Geometry



Geometry CHAPTER 4 REVIEW NAME _________________

Congruent Triangles PERIOD_____ DATE______

Classify the triangle by its sides (equilateral, isosceles, scalene) and by its angles (acute, right, obtuse, equiangular) .

_________________________1.

_________________________2. 1) 2)

_________________________3.

_________________________4.

3) 4)

_________________________5.

_________________________6. 5) 6)

Find the measure of the numbered angles.

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

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. 16)

Justify the equation.

16. Equation____________________

x=________ [pic] 17)

17. Equation____________________

x=________ [pic]

18. Equation____________________ 18)

x=________

19. Equation____________________ 19)

x=________

20. Equation____________________ 20)

x=________

In the diagram, [pic]. Complete the statement

21. [pic] 22. [pic]

23. [pic] 24. [pic]

25. [pic] 26. [pic]

27. [pic]

28. [pic]

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__________

[pic] [pic]

31. 32.

Method__________ Method__________

[pic] [pic]

33. 34.

Method__________ Method__________

[pic] [pic]

State the third congruence that is needed to prove [pic] 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

[pic] is a right angle

[pic] is a right angle

_______[pic]_______

36. Using the SAS Congruence Theorem

[pic] _______[pic]_______

37. Using the SSS Congruence Theorem

[pic]

_______[pic]_______

State the third congruence that is needed to prove [pic] 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

[pic]

_______[pic]_______

39. Using the AAS Congruence Postulate

[pic]

_______[pic]_______

Complete the following two-column proofs. Redraw triangles and label any congruent parts.

40. GIVEN: [pic]

[pic]

PROVE: [pic]

|Statements |Reasons |

| | |

|1. [pic] |1. |

|2. |2. Given |

|3. [pic] |3._________________________________ |

|4. ________________________ |4._________________________________ |

41. GIVEN: [pic] is a right angle [pic] is a right angle

[pic]

PROVE: [pic]

|Statements |Reasons |

| | |

|1. [pic] |1._________________________________ |

|2. |2. Given |

|3. [pic] is a right angle |3._________________________________ |

|[pic] is a right angle | |

|4. [pic] is a right triangle |4._________________________________ |

|[pic] is a right triangle | |

|5. |5. HL Postulate |

| | |

|6. ________________________ |6. _________________________________ |

42. Find the measure of the indicated angle or length:

[pic]

43. Find the values of x and y.

[pic]

44. Write the equation of the new line:

a) Parallel to [pic] and through point P(-5, -4)

b) Perpendicular to [pic] and through point Q(4, 5)

45. The coordinates for points A and B are, A(-2, 5) and B(8, -6). Find the distance and midpoint.

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[pic]___________________

[pic]___________________

[pic]___________________

[pic]___________________

[pic]___________________

[pic]___________________

[pic]___________________

[pic]___________________

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