Lesson 2.4 - Reasoning in Algebra
Lesson 2.5 - Proving Angles Congruent
“The other day I was driving down the road and
saw a banana peel…and swerved. Thank you
Mario Kart.”
Properties
(on theorem sheet)
Properties
(on theorem sheet)
Justifying Steps
Example: Solve for x. JUSTIFY each step.
Statement
2(x - 3) +12 = 14
2x – 6 + 12 = 14
2x + 6 = 14
2x = 8
x=4
Reason
Given

Justifying Steps
Example: Solve for x and justify each step.
B
Given:
mAOC 139
A
x
(2x+10)
C
O

Statement
mAOC 139
mAOB  mBOC  mAOC
x + 2x + 10 = 139
3x + 10 = 139
3x = 129
x = 43
Reason
Justifying Steps
Example: Solve for m and justify each step
2m
Given: XZ = 32
X
Statement
XZ = 32
XY + YZ = XZ
2m + 5m + 11 = 32
7m + 11 = 32
7m = 21
m=3
5m + 11
Y
Z
Reason
Vertical Angles Theorem
Theorem: A statement that is proven
Theorem 2.1: Vertical angles are congruent
Prove it!
Given:1 and 2
Prove: 1  2
are vertical angles
Statement
1 and 2
 are vertical angles
m1 m3  180
m2  m3 180
 m1 m3  m2  m3
m1  m2
1  2
1
3
4
2
Reason
Finding Angle Measures
Find the value of x. Then label all the angle measures.
(7x – 6)o
(2x + 9)o
Finding Angle Measures
Find the value of the variables. Then label all the angle measures
(5x + 10)o
(7x - 16)o
(7x + 2y)o
(8x + 9)o
(19x)o
Congruent Supplements Theorem
Theorem 2.2: If two angles are supplements to the same angle,
then the two angles are congruent
1 is supplementary to 2
3 is supplementary to 2

What can we 
conclude?


2
3
1
4
Congruent Complements Theorem
Theorem 2.3: If two angles are complements of the same angle then
they are congruent
Theorem 2.4: All right angles are congruent
Theorem 2.5: If two angles are congruent and supplementary, then
each is a right angle
Lesson 2.4 - Reasoning in Algebra
Lesson 2.5 - Proving Angles Congruent
HW: 2.4 # 2-22 even, 28, 44-49
2.5 # 1-3, 7-18, 21, Challenge: 30, 32
Tools: Vertical Angles Theorem, Congruent
Supplements Theorem, Congruent Complements
Theorem
“The other day I was driving down the road and
saw a banana peel…and swerved. Thank you
Mario Kart.”