Download Test Review #1-32

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. m1  _______
8. m2  _______
9. m3  _______
10. m4  _______
11. m5  _______
12. m6  _______
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=________
mBCA  ________
17)
17. Equation____________________
x=________
mBCD  ________
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. mB  _____ 26. mC  _____
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  ___________________