Given: OS with two secants, MO and NP that intersect in the interior of the circle at Q
Prove: m/MQP = (mMP+mÑO)
Statements
Reasons
1. OS with two secants, MO and NP that intersect in 1. Given
the interior of the circle at Q
2. Draw auxiliary line PO
3.m/MQP m/QPO+mZQOP
4.m/QOP=mMP; m/QPO=mNO
5. m/QOP+m/QPO=mMP+m/QPO
6.m/MQP= -mMP+mZQPO
-mMP+mNO
7.m/MQP-
8. m/MQP-
2
3.
(Hint: ZQPO and ZQOP are
remote interiors)
4.
Theorem
5. Add. Prop. of (m/QPO was
added to both sides of the equation)
6.
(from line 3)
7.
(from line 4)
(mMP+mNO)
8. Distributive Property of
Options:
Substitution
Subtraction
Inscribed
Exterior Angle Theorem.
Through any two points there is exactly one line.
Isusules
Thangle theoren
Pythagorean threarm
