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.
-----------------------
[pic]___________________
[pic]___________________
[pic]___________________
[pic]___________________
[pic]___________________
[pic]___________________
[pic]___________________
[pic]___________________
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