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Lesson 5.3 Chord & Arc Relationships
High School
Created on October 4, 2024
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Transcript
Lesson 5.3
CHORD & ARC Relationships
OBJECTIVES
- Define chord and identify chords in a circle
- Define congruent arcs
- Discover relationship between central angles and congruent arcs
- Discover relationship between congruent chords and congruent arcs
- Determine and apply properties of a perpendicular bisector of a chord
- Apply Pythagorean Theorem to determine various segment lengths within a circle
CHORD
A chord is a line segment that has both endpoints on the circle.
Practice:
Click on two chords in this circle.
NOTE:
DIAMETER
IJ is a line segment with both endpoints on the circle, but since it goes through the center K, it is called a
Since chords AB and CD are both 6 units away from the center, AB ≅CD.
CONGRUENT CHORDS
Congruent chords have the same length.
If two chords are the same distance from the center of a circle, then the chords are congruent.
Click here for a Geogebra interactive animation of this theorem!
Arcs TS and QR are both 20°
20°
Arcs PT and PR are both 90°
Arcs TPR and RST are both 180°
CONGRUENT ARCS
Arcs on the same circle that have the same measure are congruent. They can be formed by congruent central angles.
slide 4
This is the same image fromshowing congruent chords.
Since chords AB and CD are congruent, then arcs AB and CD are also congruent.
If AB ≅ CD, then AB ≅ CD
CONGRUENT ARCS
Congruent arcs are also formed by congruent chords.
RECALL:
Perpendicular bisector
A perpendicular line or segment that intersects a line segment at its midpoint.
LM is the perpendicular bisector of PQ.
RS is the perpendicular bisector of PQ.
Perpendicular Bisectors
in circles
EI is a radius of circle E.
If a radius of a circle is perpendicular to a chord, then it bisects that chord.
G is the midpoint of chord CD. CG ≅ GD
Perpendicular Bisectors
in circles
KI and KJ are radii of circle K. KI and KJ are perpendicular bisectors of chords DC and EF, respectively.
RECALL:
pythagorean theorem
hypotenuse
an equation used to solve for missing side lengths of a right triangle
Solve for x:
pythagorean theorem
in circles
EI is a radius of circle E and a perpendicular bisector of chord CD.
EG = 6 and GD = 8. Find each segment length.
Click here to reveal answers!
10
CG =
ED =
hover over each answer for an explanation!
10
16
EI =
CD =
pythagorean theorem
in circles