14 2 B TANGENT LINES TO CIRCLES PROOF
14 -2 B TANGENT LINES TO CIRCLES PROOF GEOMETRY
CENTER OF CIRCLE • To find the center of the circle through a construction • 1) Inscribe a triangle in the circle • 2) Construct the perpendicular bisectors of each of the sides of the triangle
CIRCLE CENTER AND CHORD THEOREMS: • The Perpendicular from the center of the circle to a chord bisects the chord. • The segment from the center of the circle to the midpoint of a chord is perpendicular to the chord. • The perpendicular bisector of a chord passes through the center of the circle.
CIRCLE CENTER AND CHORD THEOREMS: • Sketch out the proof for: 1)Create a circle with center P • The Perpendicular and a chord QR. Let PF befrom the centertoof the QR. circle to perpendicular chord 2) Introduce PQ and a chord radii bisects the. PR. 3) Show the two smaller triangles chord. congruent through HL.
CIRCLE CENTER AND CHORD THEOREMS: • Sketch out the proof for: 1)Create a circle with center P • The segment and a chord QR. Letfrom PF bethe center of the. QR. circle to the bisector of chord 2) Introduce PQ and PR. midpointradii of a chord is 3) Show the two smaller triangles perpendicular to the congruent chord. through SSS.
1)Create a circle with center P and a CIRCLE CENTER AND CHORD chord QR. THEOREMS: Let m be the perpendicular bisector of QR through F. 2) By the • Sketch perpendicular bisector out the proof for: theorem, any point on m is equidistant • The perpendicular from the endpoints. bisector of a chord 3) Uniqueness shown through any passesfrom through the is on point equidistant endpoints the perpendicular bisector (Thm 6 -4). center of the circle.
EQUIDISTANT CHORDS THEOREM: In the same circle or in congruent circles, chords are equidistant from the center if and only if they are congruent.
EQUIDISTANT CHORDS THEOREM: Show: IF equidistant from the center THEN congruent.
EQUIDISTANT CHORDS THEOREM: Show: IF congruent THEN equidistant from the center.
HOMEWORK Pg. 457 #16 -18 Pg. 461 #1, 5, 8
- Slides: 10