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Quizzes > High School Quizzes > Electives

Congruent Chords & Arcs Practice Quiz

Enhance geometry skills with chords and arcs worksheets

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on arcs and chords for high school geometry students.

If two chords in a circle are congruent, what can be said about the arcs they intercept?
They intercept congruent arcs
They intercept arcs with no specific relationship
They intercept supplementary arcs
They intercept unequal arcs
Congruent chords intercept arcs that are equal in measure due to the symmetry of the circle. This is a direct consequence of the properties of circles.
What is the key property of the perpendicular bisector of a chord in a circle?
It is parallel to the chord
It bisects the arc opposite to the chord
It is perpendicular to the radius
It always passes through the center of the circle
The perpendicular bisector of any chord always passes through the center of the circle. This fundamental property is often used to establish relationships between chords and the circle's center.
If two chords in a circle are congruent, then they are also:
Equidistant from the center
Perpendicular to the radius
Congruent to the diameter
Parallel to each other
In a circle, congruent chords are equidistant from the center. This theorem is a key concept in circle geometry, ensuring symmetry in the circle's structure.
A chord in a circle is defined as:
A line touching the circle at exactly one point
A ray extending from the center to the circle
A line segment with both endpoints on the circle
A complete circle
A chord is a line segment with both endpoints on the circle. This definition clearly distinguishes it from tangents and radii.
If chord AB is congruent to chord CD in a circle, what is the relationship between arc AB and arc CD?
Arc AB is congruent to arc CD
Arc AB is supplementary to arc CD
Arc AB is twice the measure of arc CD
Arc AB and arc CD have no relation
Congruent chords intercept congruent arcs in a circle. This is one of the essential properties of chords and arcs, arising from the circle's symmetry.
If two central angles in a circle intercept congruent arcs, then the angles are:
Equal to twice the arc measure
Supplementary
Congruent
Complementary
Central angles have measures that exactly match their intercepted arcs. Therefore, if the arcs are congruent, the central angles must also be congruent.
Which method can be used to prove that two chords in a circle are congruent?
All of the above
Showing that they are equidistant from the center
Showing that their intercepted arcs are congruent
Showing that their corresponding central angles are congruent
Each method provided is a valid approach to proving that two chords are congruent. They are all based on established properties of circle geometry.
What is the measure of an inscribed angle that intercepts an arc of 80°?
160°
80°
40°
20°
An inscribed angle is always half the measure of its intercepted arc. Thus, an 80° arc produces an inscribed angle of 40°.
What is the formula for calculating the length of an arc intercepted by a central angle θ (in degrees) in a circle with radius r?
L = (θ/360) à - πr
L = (θ/360) à - 2πr
L = (θ/90) à - 2πr
L = (θ/180) à - πr
The length of an arc is determined by taking the fraction of the circle's full angle (360°) that the central angle represents, and multiplying it by the circumference (2πr).
In a circle with center O, if chords AB and CD are congruent, which of the following must be true?
The intercepted arcs AB and CD are congruent
Both of the above
None of the above
The central angles AOB and COD are congruent
Congruent chords ensure that both the intercepted arcs and the central angles they subtend are congruent. Both conditions follow from the properties of circles.
In a circle with center O, if chord AB subtends an arc of 120°, what is the measure of central angle AOB?
180°
120°
240°
60°
A central angle is equal in measure to its intercepted arc. Therefore, if the arc measures 120°, the central angle also measures 120°.
Which statement accurately describes the relationship between an inscribed angle and its intercepted arc?
The inscribed angle equals the intercepted arc
There is no fixed relationship
The inscribed angle measures half the intercepted arc
The inscribed angle is twice the intercepted arc
The measure of an inscribed angle is always half of the measure of its intercepted arc. This is one of the most fundamental relationships in circle geometry.
If two chords intercept arcs that are congruent, then the chords are:
Congruent
Unrelated in length
Parallel
Equal only if one is a diameter
Congruent intercepted arcs imply that the corresponding chords are congruent. This relationship is a direct consequence of the properties of circles.
A circle is divided into 12 congruent arcs by equal chords. What is the measure of each intercepted arc?
60°
40°
30°
90°
Since the total angle around a circle is 360°, dividing by 12 results in intercepted arcs of 30° each. This division confirms the congruency of the arcs.
Which property is true for chords in a circle that are equidistant from the center?
They are congruent and subtend congruent arcs
They are equal to the diameter
They are parallel to the tangent at the circle
They have no relation
Chords that are equidistant from the center of a circle are congruent and therefore subtend congruent arcs. This is a well-established theorem in circle geometry.
In circle O, chords AB and CD are congruent. If chord AB is 8 cm long and lies 3 cm from the center, what can be inferred about chord CD?
Chord CD is 8 cm long but its distance from the center is different
Chord CD is shorter than 8 cm if placed further from the center
Not enough information to determine chord CD's position
Chord CD is also 8 cm long and is 3 cm from the center
Congruent chords in a circle are not only equal in length but also equidistant from the center. Therefore, chord CD must also be 8 cm long and lie 3 cm from the center.
In a circle with a radius of 10 cm, a chord is located 6 cm from the center. What is the approximate length of the chord?
20 cm
12 cm
16 cm
14 cm
Using the chord length formula: length = 2√(r² - d²), we substitute r = 10 cm and d = 6 cm to get 2√(100 - 36) = 2√64 = 16 cm.
Two congruent chords in a circle determine two congruent arcs. If one of these arcs measures 85°, what is the measure of an inscribed angle intercepting that arc?
170°
42.5°
85°
127.5°
An inscribed angle is always half the measure of its intercepted arc. Therefore, an arc of 85° yields an inscribed angle of 42.5°.
A circle with radius 12 cm has a chord that subtends a central angle of 150°. What is the length of this chord, approximately?
25 cm
23.2 cm
21 cm
24 cm
The chord length can be calculated using the formula: length = 2r sin(θ/2). With r = 12 cm and θ = 150°, we have 2 à - 12 à - sin(75°) which approximates to 23.2 cm.
In circle O, two chords AB and CD intersect at point E. If AB = CD and AE equals CE, what must be true about the segments BE and DE?
There is no relation between BE and DE
BE is greater than DE
BE is less than DE
BE equals DE
When two chords intersect inside a circle, the products of the segments are equal. Given that AE equals CE and the chords are congruent, it follows that BE must equal DE.
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Study Outcomes

  1. Apply properties of congruent chords and arcs to solve geometric problems.
  2. Calculate arc measurements using given angle relationships.
  3. Analyze circle diagrams to identify congruent segments and arcs.
  4. Synthesize information from multiple diagram components to determine unknown values.

Congruent Chords & Arcs Worksheet Cheat Sheet

  1. Congruent Chords and Arcs - In any circle, chords of equal length subtend arcs of equal measure, and the reverse is true too. Think of it like slicing a pizza: identical crust segments always cover the same topping arc. Explore this theorem
    2. onlinemathlearning.com
  2. Perpendicular Bisector Theorem - A radius or diameter perpendicular to a chord will cut that chord and its intercepted arc right down the middle. This is a go‑to move when you need to split pieces into perfect halves. Dive into the proof
    3. onlinemathlearning.com
  3. Equidistant Chords - If two chords sit the same distance from the center, they're twins in length. It's a quick way to spot congruent chords without measuring every angle. See it in action
    4. onlinemathlearning.com
  4. Central Angles and Arcs - The size of a central angle matches exactly the arc it intercepts. So a 60° central angle always points to a 60° piece of the circle. Get the details
    5. onlinemathlearning.com
  5. Congruent Central Angles and Chords - In the same circle (or identical circles), equal central angles guarantee equal chord lengths. Use this to link angle measures directly to distances on the circle. Learn more here
    6. onlinemathlearning.com
  6. Arcs Between Parallel Chords - When two chords are parallel, the arcs caught between them are equal. It's like railroad tracks: parallel lines trap perfectly matching arcs. Check out the scenario
    7. onlinemathlearning.com
  7. Chord Length and Distance from Center - The closer a chord is to the center, the longer it stretches across the circle. Imagine pulling a rubber band tighter towards the hub - more tension, more length! Unpack this relationship
    8. onlinemathlearning.com
  8. Inscribed Angles and Arcs - An inscribed angle measures half the arc it intercepts, so a 100° arc underwrites a 50° angle. It's a neat shortcut for angle-chasing in circle proofs. Discover the trick
    9. onlinemathlearning.com
  9. Chord Properties in Congruent Circles - In congruent circles, corresponding chords match in length every time. It's the ultimate circle‑matching game - if the circles fit, their chords do too. Find out why
    10. onlinemathlearning.com
  10. Practice Problems - Regular problem-solving cements these ideas in your brain. Grab worksheets and sample questions to turn theory into muscle memory. Start practicing now
    11. onlinemath4all.com
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