Geometry Chapter 10 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a chord?

A line that intersects a circle in two points

A chord that passes through the center of the circle

A line in the plane of a circle in exactly one point

A segment whose endpoints are points on a circle (correct)

What is a secant?

A line that intersects a circle in two points.

What is a diameter?

A chord that passes through the center of the circle.

What is a tangent?

A line in the plane of a circle that touches the circle at exactly one point. Signup and view all the answers

State Theorem 10.1.

If a line is a tangent, then the tangent line is perpendicular to the radius. Signup and view all the answers

State Theorem 10.2.

If a line is perpendicular to the radius at the endpoint, then it is a tangent. Signup and view all the answers

State Theorem 10.3.

If two segments from the same exterior point are tangent to a circle, then they are congruent. Signup and view all the answers

What is the Arc Addition Postulate (Postulate 26)?

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs: mABC = mAB + mBC. Signup and view all the answers

State Theorem 10.4.

In the same circle or congruent circles, two minor arcs are congruent if their corresponding chords are congruent. Signup and view all the answers

State Theorem 10.5.

If a diameter of a circle is perpendicular to a chord, then it bisects the chord and its arc. Signup and view all the answers

State Theorem 10.6.

If one chord is the perpendicular bisector of another chord, then the first chord is a diameter. Signup and view all the answers

State Theorem 10.7.

In the same circle or congruent circles, two chords are congruent if they are equidistant from the center. Signup and view all the answers

State Theorem 10.8.

If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc. Signup and view all the answers

State Theorem 10.9.

If two inscribed angles intercept the same arc, then the angles are congruent. Signup and view all the answers

State Theorem 10.10.

If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Signup and view all the answers

State Theorem 10.11.

A quadrilateral can be inscribed in a circle only if its opposite angles are supplementary. Signup and view all the answers

State Theorem 10.12.

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. Signup and view all the answers

State Theorem 10.13.

If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Signup and view all the answers

State Theorem 10.15.

If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Signup and view all the answers

Study Notes

Circle Terminology

Chord: A segment with endpoints on a circle.
Secant: A line that intersects a circle at two distinct points.
Diameter: A special chord that passes through the center of the circle.
Tangent: A line that touches the circle at exactly one point.

Key Theorems

Theorem 10.1: A tangent line is perpendicular to the radius at the point of tangency.
Theorem 10.2: If a line is perpendicular to a radius at its endpoint, it is a tangent line.
Theorem 10.3: Tangent segments drawn from the same exterior point to a circle are congruent.
Theorem 10.4: In the same or congruent circles, two minor arcs are congruent if their corresponding chords are congruent.
Theorem 10.5: A diameter that is perpendicular to a chord bisects both the chord and its arc.
Theorem 10.6: If one chord is the perpendicular bisector of another, then the first chord must be a diameter.
Theorem 10.7: Two chords are congruent if they are equidistant from the center of the circle.

Angles and Arcs

Theorem 10.8: An inscribed angle measures half that of its intercepted arc.
Theorem 10.9: Inscribed angles that intercept the same arc are congruent.
Theorem 10.10: An inscribed right triangle has its hypotenuse as the diameter of the circle.
Theorem 10.11: A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Intersecting Chords and Angles

Theorem 10.12: The angle formed by a tangent and a chord at the point of intersection is half the measure of the intercepted arc.
Theorem 10.13: For two intersecting chords in a circle, each angle's measure is half the sum of the measures of the intercepted arcs and their vertical angles.
Theorem 10.15: The product of the lengths of segments of one chord equals the product of the lengths of segments of another chord intersecting inside the circle.

Additional Theorems

Theorem 10.14 and Theorem 10.16-10.17 are not defined in the provided text.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge of key concepts in geometry with these flashcards focused on Chapter 10. Learn important terms like chord, secant, diameter, and tangent, alongside relevant theorems. Perfect for review before an exam or as a study aid!