Five-Minute Check (over Lesson 10–2)
NGSSS
Then/Now
Theorem 10.2
Proof: Theorem 10.2 (part 1)
Example 1: Real-World Example: Use Congruent Chords to Find
Arc Measure
Example 2: Use Congruent Arcs to Find Chord Lengths
Theorems
Example 3: Use a Radius Perpendicular to a Chord
Example 4: Real-World Example: Use a Diameter Perpendicular to
a Chord
Theorem 10.5
Example 5: Chords Equidistant from Center
Over Lesson 10–2
A. 105
0%
B
D. 124
A
0%
A
B
C
0%
D
D
C. 118
C
B. 114
A.
B.
C.
0%
D.
Over Lesson 10–2
A. 35
0%
B
D. 72
A
0%
A
B
C
0%
D
D
C. 66
C
B. 55
A.
B.
C.
0%
D.
Over Lesson 10–2
A. 125
0%
B
D. 140
A
0%
A
B
C
0%
D
D
C. 135
A.
B.
C.
0%
D.
C
B. 130
Over Lesson 10–2
A. 160
D. 130
0%
B
A
0%
A
B
C
D
D
C. 140
A.
B.
C.
D.
C
B. 150
0%
0%
Over Lesson 10–2
A. 180
D. 210
0%
B
A
0%
A
B
C
D
D
C. 200
A.
B.
C.
D.
C
B. 190
0%
0%
Over Lesson 10–2
Dianne runs around a circular track that has a
radius of 55 feet. After running three quarters of the
distance around the track, how far has she run?
A. 129.6 ft
0%
B
D. 345.6 ft
A
0%
A
B
C
0%
D
D
C. 259.2 ft
C
B. 165 ft
A.
B.
C.
0%
D.
MA.912.G.6.2 Define and identify:
circumference, radius, diameter, arc, arc
length, chord, secant, tangent and concentric
circles.
MA.912.G.6.4 Determine and use measures
of arcs and related angles.
Also addresses MA.912.G.6.3.
You used the relationships between arcs and
angles to find measures. (Lesson 10–2)
• Recognize and use relationships between
arcs and chords.
• Recognize and use relationships between
arcs, chords, and diameters.
Use Congruent Chords to Find
Arc Measure
Jewelry A circular piece of jade is hung from a
chain by two wires around the stone.
JM  KL and
= 90. Find
.
Use Congruent Chords to Find
Arc Measure
A. 42.5
0%
B
0%
A
D. 170
A
B
C
0%
D
D
C. 127.5
A.
B.
C.
0%
D.
C
B. 85
Use Congruent Arcs to Find Chord Lengths
Use Congruent Arcs to Find Chord Lengths
WX = YZ
7x – 2 = 5x + 6
2x = 8
x =4
Definition of congruent segments
Substitution
Add 2 to each side.
Divide each side by 2.
So, WX = 7x – 2 = 7(4) – 2 or 26.
Answer: WX = 26
A. 6
0%
B
0%
A
D. 13
A
B
C
0%
D
D
C. 9
A.
B.
C.
0%
D.
C
B. 8
Use a Radius Perpendicular to a Chord
Answer:
A. 14
B. 80
0%
B
A
0%
A
B
C
0%
D
D
D. 180
C
C. 160
A.
B.
C.
0%
D.
Use a Diameter Perpendicular to a
Chord
CERAMIC TILE In the ceramic stepping stone
below, diameter AB is 18 inches long and chord EF
is 8 inches long. Find CD.
Use a Diameter Perpendicular to a
Chord
Step 1
Draw radius CE.
This forms right ΔCDE.
Use a Diameter Perpendicular to a
Chord
Step 2
Find CE and DE.
Since AB = 18 inches, CB = 9 inches. All
radii of a circle are congruent, so
CE = 9 inches.
Since diameter AB is perpendicular to EF,
AB bisects chord EF by Theorem 10.3. So,
1 (8) or 4 inches.
DE = __
2
Use a Diameter Perpendicular to a
Chord
Step 3
Use the Pythagorean Theorem to find CD.
CD2 + DE2 = CE2 Pythagorean Theorem
CD2 + 42 = 92
Substitution
CD2 + 16 = 81
Simplify.
CD2 = 65
Answer:
Subtract 16 from each
side.
Take the positive
square root.
In the circle below, diameter QS is 14 inches long
and chord RT is 10 inches long. Find VU.
A. 3.87
0%
B
0%
A
D. 5.32
A
B
C
0%
D
D
C. 4.90
A.
B.
C.
0%
D.
C
B. 4.25
Chords Equidistant from Center
Since chords EF and GH are congruent, they are
equidistant from P. So, PQ = PR.
Chords Equidistant from Center
PQ = PR
4x – 3 = 2x + 3
x =3
So, PQ = 4(3) – 3 or 9
Answer: PQ = 9
Substitution
Simplify.
A. 7
B. 10
0%
B
A
0%
A
B
C
0%
D
D
D. 15
C
C. 13
A.
B.
C.
0%
D.