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Geometry Chapter 5 Review
Classify each triangle by its sides and by the measure of its angles.
1.
2.
3.
Find the value of x and the length of each side.
4.
5.
Given that PQRS  WXYZ, find the corresponding parts.
6. P  ___
10. PS  ___
7. RS  ___
11. X  ___
8. XY  ___
9. Y  ___
12. QPSR  ___ 13. YXWZ  ___
14. In ! DEF , find DE.
15. One of the acute angles in a right triangle has a measure of 35. What is the measure of the other acute angle?
16. The vertex angle of an isosceles triangle is 58. What are the measures of
the base angles?
Find the measure of the missing angles.
17. m1
18. m2
19. m3
20. m4
21. m5
Decide whether the triangles can be proven congruent by a postulate or theorem. If they can, state the
postulate or theorem that can be used.
22.
23.
24.
25.
Use the diagram to write a two-column proof.
26. Given OM bisects AOB and MO bisects AMB
Prove ! AMO  ! BMO
27. Given AB  AC and BAD  CAD
Prove BD  CD
Review Answers:
3.
isosceles obtuse
4. x  1.5, RQ  3.9, RP  3.9, PQ  1.6
5.
x  9, all side lengths  26
6. W
9.
R
WZ
11.
14.
x  1, DE  11 15.
55
18. 62.5
19.
55
22. yes; SAS Congruence Theorem (Thm. 5.5)
23.
yes; HL Congruence Theorem (Thm. 5.9)
24. yes; AAS Congruence Theorem (Thm. 5.11)
25.
No
1.equilateral equiangular
7. YZ
12. XWZY
16. 61
26.
27.
2. scalene obtuse
8. QR
13. RQPS
17. 62.5
STATEMENTS
REASONS
1. OM bisects  AOB
1. Given
2.  AOM   BOM
2. Definition of
angle bisector
3. MO bisects  AMB
3. Given
4.  AMO   BMO
4. Definition of
angle bisector
5. MO  MO
5. Reflexive Property
of Segment
Congruence
(Thm. 2.1)
6. ! AMO  ! BMO
6. ASA Congruence
Theorem
(Thm. 5.10)
STATEMENTS
REASONS
1. AB  AC
1. Given
2. AB  AC
2. Definition of
congruent segments
3.  BAD  CAD
3. Given
4. AD  AD
4. Reflexive Property of
Segment Congruence
(Thm. 2.1)
5. ! ABD  ! ACD
5. SAS Congruence
Theorem (Thm. 5.5)
6. BD  CD
6. Corresponding parts
of congruent triangles
are congruent
7. BD  CD
7. Definition of
congruent
segments
10.
20.
75
21.
Q
50
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