Download 5.5 Notes

Expectations/Procedures
Triangle Congruency
(Geometry Review)
Four triangle congruence theorems:
We can use trigonometry to find the other parts
of the triangle once congruence is established.
Law of Sines
Given any ABC with angles A,B,C and opposite
sides a,b,c respectively.
𝑠𝑖𝑛𝐴
𝑎
=
𝑠𝑖𝑛𝐵
𝑏
=
𝑠𝑖𝑛𝐶
𝑐
• Use when you have AAS or ASA to find the other
side lengths.
• Use when you have SSA to find the angle
opposite the other given side.
Example (AAS)
Solve ABC given A = 38 B = 46 and a = 9.
Example – You Try (ASA)
Solve ABC given A = 60 B = 45 and c = 5.1
SSA Case
• Since SSA does not determine its size and
shape, there might be one, two, or zero
triangles determined.
Example (SSA)
State whether the given measurements determine
zero, one, or two triangles. Then solve the triangle.
A = 73 a = 24 and b = 28
Example (SSA)
State whether the given measurements
determine zero, one, or two triangles. Then
solve the triangle.
B = 82 b = 17 and c = 15
Example (SSA)
State whether the given measurements
determine zero, one, or two triangles. Then
solve the triangle.
A = 30 a = 6 and b = 7
Example
• A forest ranger at station A sights a fir in the
direction 32 east of north. A second forest
ranger at station B, 10 miles due east of A,
sights the same fire on a line 48 west of
north. Find the distance from each ranger
station to the fire.
Homework
• 5.5 (pg. 439) #4,6,14-16,37