5.1.1 Perpendicular and Angle Bisector Theorems − Worksheet
Example 1: Use the diagram for Exercises 1-3. 1. Given that PS = 53.4, QT = 47.7, and QS = 53.4, find PQ .
m
T
P
Q
S
2. Given that m is the perpendicular bisector of PQ and SQ = 25.9, find SP .
3. Given that m is the perpendicular bisector of PQ , PS = 4 a , and QS = 2 a + 26, find QS .
Example 2: Use the diagram for Exercises 4-6. 4. Given that BD bisects ∠ ABC and CD = 21.9, find AD .
5. Given that AD = 61, CD = 61, and m ∠ ABC = 48º, find m ∠ CBD .
6. Given that DA = DC , m ∠ DBC = (10 y + 3)º, and m ∠ DBA = (8 y + 10)º, find m ∠ DBC .
L
7. For a king post truss to be constructed correctly, P must lie on the bisector of ∠ JLN . How can braces PK and PM be used to ensure that P is in the proper location?
K
M
J
N
P
Example 3: Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints. 8. M ( − 5, 4), N (1, − 2) 9. U (2, − 6), V (4, 0) 10. J ( − 7, 5), K (1, − 1)
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