Are chords and arcs congruent?
1. Chord Theorem #1: In the same circle or congruent circles, minor arcs are congruent if and only if their corresponding chords are congruent. Chord Theorem #3: If a diameter is perpendicular to a chord, then the diameter bisects the chord and its corresponding arc.
Do congruent circles have congruent arcs?
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. “q → p” If two chords are congruent in the same circle or two congruent circles, then the corresponding minor arcs are congruent.
Are chords in a circle equal?
In circles Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle.
What do congruent circles have congruent?
Q. Congruent circles are two or more circles that have congruent radii. In Figure 6.3, circles P and Q are congruent because their radii have equal lengths. Concentric circles are coplanar circles that have a common center.
How do you prove a chord is congruent?
If two chords are congruent, then their corresponding arcs are congruent. If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. In the same circle or congruent circle, two chords are congruent if and only if they are equidistant from the center.
How do you know if two circles are congruent?
Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference.
How do you prove a chord?
The Intersecting Chords Theorem asserts the following very useful fact: Given a point P in the interior of a circle with two lines passing through P, AD and BC, then AP*PD = BP*PC — the two rectangles formed by the adjoining segments are, in fact, equal.
What is the symbol of congruent?
The symbol ≡ means “is congruent to”. Two triangles are similar if they have the same shape. Two similar triangles are equiangular, i.e., angles which correspond are equal.
What is 9th Theorem?
Theorem 9: In a parallelogram, opposite sides are equal and opposite angles are equal.