Download Questions on 2.4 Grading 2.4

September 15, 2014
Questions on 2.4
Grading 2.4
10. B
21. true
11. False, example
22. true
12. true
23. false
13. false, example
24. C
14. true
46. 27
15. false
47. 32
16. false
48. 18
17. false
49. 23
18. false
50. 74
19. true
51. 4
20. false
56. 18, 162
September 15, 2014
2.5
Reason Using Properties
from Algebra
Algebraic Properties of EqualityLet a, b, and c be real numbers.
Addition Property
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a - c = b - c
Multiplication Property
If a = b, then ac = bc
Division Property
a b
If a = b and c ≠ 0, then c = c
Substitution Property
If a = b, then a can be substituted for b in any
equation or expression.
Ex 1) Solve 2x + 5 = 20 - 3x. Write a reason for each step.
September 15, 2014
Distributive Propertya(b + c) = ac + bc, where a, b, and c are real numbers.
Reflexive Property of EqualityReal Numbers
Segment Length
Angle Measure
For any real number a, a = a
For any segment AB, AB = AB
For any angle A, m A = m A
Symmetric Property of EqualityReal Numbers
Segment Length
Angle Measure
For any real numbers a and b, if a = b then b = a
For any segments AB and CD, if AB = CD, then
CD = AB
For any angles A and B, if m A = m B, then
m B=m A
Transitive Property of EqualityReal Numbers
Segment Length
Angle Measure
For any real numbers a, b and c, if a = b and b = c, then
a=c
For any segments AB, CD, and EF, if AB = CD and
CD = EF, then AB = EF
For any angles A, B, and C, if m A = m B, and
m B = m C, then m A = m C
Postulate 4: Angle Addition PostulateIf P is in the interior of
RST, then the m
m RSP and
PST.
m
RST = m
RSP = m
PST
RST is equal to the sum of the
R
S
P
T
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.
A
B
C
September 15, 2014
Ex 2) Use the property to complete the statement.
Substitution Property of Equality: If AB = 20, then AB + CD = ____.
Symmetric Property of Equality: If m 1 = m 2, then _______.
Transitive Property of Equality: If m 1 = m 2 and m 2 = m 3, then
_______.
Ex 3) Use the diagram to determine whether m EBA = m DBC. Explain your
steps.
E
D
A
C
B
September 15, 2014
Assignment
pg. 108
#4-6all, 21-25all, 39, 40