0
What else can I help you with?
Assume that two chords in a given circle are the same distance from the center of the circle Which of the following must also be true?
They must be congruent.
Two chords that are the same distance from the center of a circle must be?
congruent
What must be true before using corresponding parts of congruent triangles are congruent in a proof?
The triangles must be congruent.
Does a diameter that is perpendicular to a chord bisect the chord?
Yes, any diameter which is perpendicular to a chord bisects said chord. This can be proved most easily with a picture, but is proved using a congruent triangle proof. Both triangles include the points at the center of the circle and the intersection of the diameter and chord. The other points should be the endpoints of the chord. They are congruent by hypotenuse leg; it was given that they are right triangle by the "perpendicular", the "leg" is the segment between the center of the circle and the intersection, and it is equal in both triangles because it is the same segment in both triangles. The hypotenuses are equal because both are radii of the circle. Because the triangles are congruent, their sides must be so the two halves of the chord are congruent, and therefore the chord is bisected by the diameter.
Are points of a circle coplanar?
Yes. A circle is defined as the set of all points in a plane equidistant from a given point (the center of the circle) - hence - all points of a circle must be co-planar by definition.
Assume that two chords in a given circle are the same distance from the center of the circle Which of the following must also be true?
They must be congruent.
Two chords that are the same distance from the center of a circle must be?
congruent
What Prove that if two chords of a circle bisect each other then the two chords are diameter of the given circle?
If two chords of a circle bisect each other, they must intersect at a point that is equidistant from both endpoints of each chord. By the properties of circles, the perpendicular bisector of any chord passes through the center of the circle. Since the two chords bisect each other at the same point and are both perpendicular to the line connecting their endpoints, this point must also be the center of the circle, making both chords diameters of the circle. Thus, if two chords bisect each other, they are indeed diameters of the circle.
For two arcs to be congruent what conditions must be met?
they must be in the same circle or congruent circles they must have the same central angle measure
Is two arcs of a circle congruent if and only if their associatd radii are congruent?
Yes, two arcs of a circle are congruent if and only if their associated radii are congruent. This is because congruent arcs subtend equal angles at the center of the circle, which means the radii connecting the center to the endpoints of the arcs must also be equal in length. Thus, the congruence of the arcs directly correlates to the congruence of their respective radii.
What are reasons used to proof that the equilateral triangle construction actually constructs an equilateral triangle?
all the angles measure up to be the sameTwo segments that are both congruent to a third segment must be congruent to each otherAll of the radii of a circle are congruent
What must be true before using corresponding parts of congruent triangles are congruent in a proof?
The triangles must be congruent.
Angles that are congruent and supplementary must be?
Angles that are congruent and supplementary must be right angles.
Does a diameter that is perpendicular to a chord bisect the chord?
Yes, any diameter which is perpendicular to a chord bisects said chord. This can be proved most easily with a picture, but is proved using a congruent triangle proof. Both triangles include the points at the center of the circle and the intersection of the diameter and chord. The other points should be the endpoints of the chord. They are congruent by hypotenuse leg; it was given that they are right triangle by the "perpendicular", the "leg" is the segment between the center of the circle and the intersection, and it is equal in both triangles because it is the same segment in both triangles. The hypotenuses are equal because both are radii of the circle. Because the triangles are congruent, their sides must be so the two halves of the chord are congruent, and therefore the chord is bisected by the diameter.
If one side of a quadrilateral is congruent can it be always parallelograms be congruent?
One side cannot be congruent: it must be congruent to something!
What makes two heptagons congruent?
The seven sides, in order, must be congruent, as must the seven angles.
What conditions must be met for two arcs to be congruent?
Two arcs are congruent if they have the same measure in degrees or radians and are parts of the same circle or circles of equal radius. Additionally, if the arcs are on different circles, they must subtend the same central angle. This ensures that the lengths of the arcs are equal, meeting the congruence condition.
