Homework Answers
1. True
2. False
- It isn’t just ANY 3 points. Point B has to lie BETWEEN A and C.
3. True
4. False
- In geometry “determine” means that it forms EXACTLY one figure. 3
NONCOLLINEAR points determine a plane, but 3 collinear points do
not.
5. False
- Through any two points there is exactly one line
6. True
7. True
8. True
9. False
- Through a line and a point OUTSIDE THE LINE exactly one plane is
determined.
10. False
- Three points either determine exactly one plane or, if they are collinear,
define infinite planes. Therefore, they are always coplanar.
11. True
12. False
- The angles would add up to 90, not 180
1. m  1 = m  2
1 2
GIVEN
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
2. m  1 + m  5 = 90 degrees
 1 and  5 are complementary angles
GIVEN
Definition of Complementary Angles
(Complementary Angles-Two angles whose
measures have a sum of 90 degrees.)
3.  1 and  7 form a linear pair
 1 and  7 are supplementary angles
GIVEN
Linear Pair Theorem
(LPT-If two angles form a linear pair then
they are supplementary.)
Definition of Supplementary Angles
(Supplementary Angles-Two angles whose
measures have a sum of 90 degrees.)
m  1 + m  7 = 180 degrees
4.  8 is a right angle and  9 is a right angle
GIVEN
m  8 = 90 degrees m  9= 90 degrees
Definition of Right Angles
(Right Angle- An angle that measures 90
degrees)
m8  m9
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
5.  4 and  7 are complementary
m  4 + m  7 = 90 degrees
6.
1  7
m1 = m7
7. m  1 + m  4 = 180 degrees
 1 and  4 are supplementary angles
GIVEN
Definition of Complementary Angles
(Complementary Angles-Two angles whose
measures have a sum of 90 degrees.)
GIVEN
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
GIVEN
Definition of Supplementary Angles
(Supplementary Angles-Two angles whose
measures have a sum of 90 degrees.)
8.  8 and  9 are vertical angles
8 9
m8 = m9
9.  3 and  8 are supp. angles
m  3 + m  8 = 180 degrees
GIVEN
Vertical Angles Theorem
(VAT-Vertical Angles are Congruent.)
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
GIVEN
Definition of Supplementary Angles
(Supplementary Angles-Two angles whose
measures have a sum of 90 degrees.)
10.  8 and  10 are both complementary to  7
GIVEN
Congruent Complements Theorem
 8   10
(CST-If two angles are complementary to
the same angle then the two angles are
congruent.)
11.  1 and  2 are supplementary
m  1 + m  2 = 180 degrees
GIVEN
Definition of Supplementary Angles
(Supplementary Angles-Two angles whose
measures have a sum of 90 degrees.)
12.  ABC is a right angle
m  ABC = 90 degrees
GIVEN
Definition of a right angle
(Right Angle- An angle that measures 90
degrees)
13. DB = SG
DB  SG
GIVEN
Definition of congruent segments
(Congruent Segments- Segments that have
the same length.)
14. MA  TH
MA = TH
GIVEN
Definition of Congruent Segments
(Congruent Segments- Segments that have
the same length.)
15. m  ABC = 147 degrees;
m  JLM = 147 degrees
m  ABC = m  JLM
 ABC   JLM
16. TI = FG, FG = SD
TI = SD
17.  DMB is a right angle
m  DMB = 90 degrees
18.  3 and  7 are comp;
 6 and  7 are comp
3  6
m3 = m6
19.  QWE and  MNB are supp;
 WSZ and  MNB are supp
 QWE   WSZ
m  QWE = m  WSZ
GIVEN
Transitive property of Equality
(If a = b and b= c then a = c)
(Technically could be substitution also)
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
GIVEN
Transitive property of Equality
(If a = b and b= c then a = c)
GIVEN
Definition of a right angle
(Right Angle- An angle that measures 90
degrees)
GIVEN
Congruent Complements Theorem
(CCT-If two angles are complementary to
the same angle then the two angles are
congruent.)
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
GIVEN
Congruent Supplements Theorem
(CST-If two angles are supplementary to the
same angle then the two angles are
congruent.)
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
20. m  7 = 30 degrees
m  8 = 30 degrees
m7 = m8
7  8
GIVEN
Transitive Property of Equality
(If a = b and b= c then a = c)
(Technically this could be substitution also)
Definition of Congruent Angles
21.  1   8
m1 = m8
GIVEN
Definition of Congruent Angles
(Congruent angles - Angles that have the
same measure.)
22. AB = DC; DC = EF; EF =GH; GH =IJ
AB = IJ
GIVEN
Transitive Property of Equality
(If a = b and b= c then a = c)