Grade 9 Circle Proofs Worksheet
This worksheet focuses on proving theorems related to circles, including properties of tangents, chords, and inscribed angles, suitable for Grade 9 Geometry students.
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Grade 9 Circle Proofs Worksheet
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Read each question carefully and provide clear, logical proofs or answers. Show all your work.
1. Prove that the tangent to a circle is perpendicular to the radius at the point of tangency.
2. Complete the proof: A perpendicular from the center of a circle to a chord the chord.
Given: Circle with center O, chord AB, and OM ⊥ AB.
To Prove: AM = MB.
Proof:
Draw radii OA and OB. In ΔOMA and ΔOMB:
OA = OB ( )
OM = OM ( )
∠OMA = ∠OMB = 90° ( )
Therefore, ΔOMA ≅ ΔOMB by .
Hence, AM = MB ( ).
3. Which theorem states that the measure of an inscribed angle is half the measure of its intercepted arc?
Tangent-Radius Theorem
Inscribed Angle Theorem
Chord-Chord Theorem
Secant-Tangent Theorem
4. Prove that the opposite angles of a cyclic quadrilateral are supplementary.
5. An angle inscribed in a semicircle is always a right angle.
True
False