Download 10.6 Day 1: Date: ______ Geometry Congruent circles have

10.6 Day 1: _______________________________________________
Geometry
Date: __________
Congruent circles have congruent __________. A ___________ __________ is an angle whose vertex
is the center of the circle.
ARCS:
________________________ : Half of a circle
________________________ : An arc smaller than a semicircle
________________________ : An arc larger than a semicircle
Ex 1). Naming Arcs
a). What are the minor arcs of ⨀𝐶?
b). What are the semicircles of ⨀𝐶?
c). What are the major arcs of ⨀𝐶 that contain point 𝐵?
Ex 2). Measures of Arcs: What are the measures of each arc in ⨀𝑂?
̂
a). 𝑇𝑂𝑈
̂
b). 𝑇𝑈𝑅
̂
c). 𝑆𝑇𝑈
̂
d). 𝑅𝑂𝑈
NAMING ARCS:
Ex 3). Measures of Arcs: What are the measures of each arc in ⨀𝐴?
̂
a) 𝐸𝐷
̂
b) 𝐸𝐹
̂
c) 𝐸𝐷𝐶
̂
d) 𝐸𝐹𝐶
Ex 4). Find the value of the variable.
Homework: pg. 688 #1 – 8, 10 – 26(e)
10.6 Day 2: _______________________________________________
Geometry
Date: __________
Coplanar circles that have the same __________
are __________________ ______________.
Ex 1). A merry-go-round has a set of seats that are 7 ft from the center of the ride and a set of
seats that are 10 ft from the center. How much farther does a child seated on the outside loop
travel that a child seated on the inside loop in one complete revolution?
ARC LENGTH:
Ex 2). What is the length of each arc? Leave your answer in terms of 𝝅.
a)
𝐴𝑟𝑐 𝐶𝐷
b)
𝐴𝑟𝑐 𝑆𝑇𝑅
c)
𝐴𝑟𝑐 𝑉𝑆𝑈
d)
𝐴𝑟𝑐 𝑉𝑈𝑇
Homework: pg. 693 #1 – 8, 10 – 14, 24
12.1 Day 1: _________________________________________
Geometry
Date: __________
Tangent Line: A line that intersects
a circle in __________ _____ place.
Theorem 12-1
If …
then …
̅̅̅̅ 𝑎𝑛𝑑 𝐴𝐺
̅̅̅̅ are tangent to ⨀𝑂. What is the value of x?
Ex 1). If 𝐴𝐷
Ex 2). Find the value of x.
a)
b)
c)
Theorem 12-2
If …
then …
Ex 3). Find the value of x.
Ex 4). Find the value of r.
a)
Homework: pg. 805 #1 – 14
b)
c)
12.1 Day 2: _________________________________________
Geometry
Date: __________
Ex 1). Determine if the line is a tangent:
a)
b)
c)
Theorem 12-3:
If …
then …
Ex 2). Find the perimeter of the triangle.
a)
b)
Ex 3). TY and ZW are diameters of
Homework: pg. 810 #1 – 8, 11, 12
S. TU and UX are tangents of
S. What is mSYZ?
12.2 Day 1: _________________________________________
Geometry
CHORD:
Several relationships between chords, arcs, and the central angles of a circle
are listed below. The converses of these theorems are also true.
Theorem 12-4
Congruent central angles have congruent arcs.
Theorem 12-5
Congruent central angles have congruent chords.
Theorem 12-6
Congruent chords have congruent arcs.
Theorem 12-7
Chords equidistant from the center are congruent.
Ex 1). In the diagram, ̅̅̅̅
𝑉𝑇 ≅ ̅̅̅̅
𝑅𝑃. What can you conclude?
Ex 2). In the diagrams the circles are congruent. What can you conclude?
a)
b)
Date: __________
Ex 3). Find the value of the variable.
a)
b)
c)
d)
Homework: pg. 816 #1 – 10 (draw the diagrams and write descriptions)
12.2 Day 2: _________________________________________
Geometry
Date: __________
Useful relationships between diameters, chords, and arcs are listed below. To
bisect a figure means to divide it exactly in half.
Theorem 12-8
In a circle, if a diameter is perpendicular to a chord, it bisects that chord
and its arc.
Theorem 12-9
In a circle, if a diameter bisects a chord that is not a diameter of the , it is
perpendicular to that chord.
Theorem 12-10
If a point is an equal distance from the endpoints of a line segment, then
that point lies on the perpendicular bisector of the segment.
Ex 1). Find the value of the variable:
a)
b)
c)
d)
e)
f)
Ex 2). Find the measure of each segment to the nearest tenth.
a)
Find c when r = 6 cm and d = 1 cm
b)
Find d when r = 10 in and c = 10 in
Homework: pg. 820 #1, 4 – 7, 10 – 14, 19 – 21
12.3 Day 1: _________________________________________
Geometry
Date: __________
Inscribed Angles
Theorem 12-11: The measure of an inscribed angle is ________ the measure of its intercepted arc.
Corollary 1:
Two inscribed angles that
intersect the same arc
are congruent.
Corollary 2:
An angle inscribed in a
semicircle is a right angle.
Corollary 3:
The opposite angles of a
quadrilateral inscribed in
a circle are supplementary.
Theorem 12-12: The measure of an angle formed by a ____________ and a ________ is half the
measure of the intercepted arc.
Ex 1). What are the values of a and b?
Ex 2). What is the measure of each numbered angle?
a)
b)
⃑⃑⃑⃑⃑ is tangent to ⨀𝐽. What is the 𝑚∠𝐴𝐵𝐶?
Ex 3). Quadrilateral ABCD is inscribed in ⨀𝐽. ∠𝐴𝐷𝐶 = 68°, 𝐶𝐸
̂ ? What is 𝑚∠𝐷𝐶𝐸?
What is 𝑚𝐶𝐵
Ex 4). Find the value of each variable:
a)
b)
c)
d)
Homework: pg. 825 #1 – 14
12.3 Day 2: _________________________________________
Geometry
Date: __________
Ex 1). Find the measure of each numbered angle:
a)
b)
c)
d)
e)
f)
g)
h)
Homework: pg. 828 #1, 3 – 8, 12, 13, 16 – 18