Download Lesson 10.05H MAIN IDEA (page #) DEFINITION OR SUMMARY

Lesson 10.05H
MAIN IDEA (page #)
DEFINITION OR SUMMARY
____________
The measure of an arc formed by two ____________ arcs is
the sum of the measures of the two arcs.
EXAMPLE or DRAWING
(P1)
mPQ + m____________ = mPQR
Congruent Arcs Theorem
(P1)
In the same circle or in two congruent circles, two arcs are
congruent if and only if their ____________________.
In circle C, WZ
ZY and WX
Inscribed Angle Theorem
(P1)
The measure of an ____________ is ____________ the
measure of its ____________.
m∠DEF =
m____________
YZ
Lesson 10.05H
Congruent Inscribed Angles
Theorem
(P1)
If ____________ of a circle or congruent circles intercept
____________ or the same arc, then the angles are ____________.
∠PQS and ∠PRS intercept PS.
∠PQS ∠____________
Inscribed Angle to a Semicircle
Theorem
(P1)
If an inscribed angle intercepts a ____________, then the
angle is a right angle.
m∠ABD = ____________
Inscribed Quadrilateral
Theorem
If a quadrilateral is ____________ in a circle, then its
opposite angles are ____________.
(P1)
m∠Q + m____________ = 180°
m____________ + m____________ = 180°
Lesson 10.05H
STEP 1
You are given an image and the fact that segment AB is
congruent to segment ____________.
First, set up the two-column table by filling in the given
information.
STEP 2
Remember, all radii of the same circle are equal in length.
Therefore, segments CA, ____________, CX, and
____________ are all congruent.
Congruent Arcs and Chords
Theorem
(P2)
STEP 3
Next, by the SSS postulate, triangles ____________ and
____________ are congruent.
STEP 4
Knowing that triangle ____________ is congruent to triangle
____________, you can state angle ACB is congruent to angle
XCY by ____________, which states that corresponding parts
of congruent triangles are congruent.
STEP 5
The last step would state that arc ____________ is
congruent to arc ____________ because of the Congruent
Arcs Theorem, which states that two arcs are congruent if
the central angles that intercept them are also congruent.
Applying the Perpendicular
Diameters and Chords Theorem
(P3)
Segments AM and MB are equal in length as are the lengths
of arcs EA and EB. Therefore, CE bisects AB at point M. AB
also bisects arc AB at point E. This illustrates the
Perpendicular Diameters and Chords Theorem, which states
that if a diameter is ____________ to a chord, then the
diameter ____________ the chord and the minor arc
between the endpoints of the chord.
Given: Circle C with congruent chords AB and
XY.
Prove: AB XY
Lesson 10.05H