Top Drawer Teachers: Two proofs of the angle sum of a triangle
19
The Angle Sum of a Triangle
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Transcript of Top Drawer Teachers: Two proofs of the angle sum of a triangle
The Angle Sum of a Triangle
Prove that x + y + z = 180°
A
B
C
x
y
z
Construct PQ through A so that PQ||BC
A
B
C
Q
P
x
y
z
∠PAB = y°(alternate angles, PQ||BC)
A
B
C
Q
P
x
y
z
y
∠QAC = z°(alternate angles, PQ||BC)
A
B
C
Q
P
x
y
z
zy
Now PAQ is a straight line
A
B
C
Q
P
x
y
z
zy
x + y + z = 180°(PAQ is a straight line)
A
B
C
Q
P
x
y
z
zy
x + y + z = 180°
A
B
C
x
y
z
The angle sum of a triangle is 180°
A
B
C
x
y
z
A different proof for the same result
Prove that x + y + z = 180°
A
B
C
x
y
z
Produce BC to P
A
B
C P
x
y
z
At C construct CQ||BA
A
B
C
Q
P
x
y
z
∠ACQ = x°(alternate angles, PQ||BC)
A
B
C
Q
P
x
y
z x
∠PCQ = y° (corresponding angles, PQ||BC)
A
B
C
Q
P
x
y
z yx
Now BCP is a straight line
A
B
C
Q
P
x
y
z yx
A
B
C
Q
P
x
y
z yx
x + y + z = 180°(BCP is a straight line)
x + y + z = 180°A
B
C
x
y
z
The angle sum of a triangle is 180°
A
B
C
x
y
z
