23. Consider a circle or congruent circles, and explain why each statement is true: a) Congruent arcs have congruent central angles. b) Congruent central angles have congruent arcs. c) Congruent chords have congruent arcs. d) Congruent arcs have congruent chords. e) Congruent central angles have congruent chords. f) Congruent chords have congruent central angles.

Q: D. Given circle O. AB BC. If mAB = 56°, what is MZAOB? What is mAC? Which chords are congruent?

A: We can find the answer as below for all the questions asked.

Q: If a quadrilateral is inscribed in a circle, then its opposite angles are angles. * O equal O right…

A:

Q: if circles G and are congruent, what can you conclude about OG and OE?

A:

Q: Consider parallel lines cut by a transversal.

A: Here we have to explain which theorems, definitions, or combinations of both can be used to prove…

Q: Which of these needs to be completed first in order to construct a circle that inscribes a triangle?

A: We needs to be completed first in order to construct a circle that inscribes a triangle is

Q: Select the most precise definition of a circle from the definitions that are given.

A: Definition of the circle

Q: show that all involutes of the circle are congruent

A: Show that: All involutes of the circle are congruent.   Note that, the involute of a circle can be…

Q: If two inscribed angles of a circle intercept the same arc, these angles are congruent. true or…

A:

Q: Prove if 2 parallel lines intersect a circle, then the intersected arcs between the lines are…

A:

Q: Prove that the angle substended by an arc of a circle at the centre is doubled the angle substended…

A: Let O be the center of circle. PQ is an arc subtending ∠POQ at the center O. To prove: ∠POQ=2∠PAQ

Q: In Case 2-(Center of the circle within the angle), Theorem 42-(An angle inscribed in a circle is…

A: Consider the provided information and diagram,

Q: Determine the measure of one interior angle of a regular 90-sided polygon.

A: We have a given polygon with 90 sides It is a regular polygon   We have to determine the measure…

Q: 8. Draw perpendicular bisectors for each of the 4 sides of the rectangle below, using the fewest…

A:

Q: What is the sum of the exterior angle measure in any polygon?

A: Topic: geometry

Q: Prove that any angle bisector of a triangle separates the opposite side into segments whose lengths…

A:

Q: Define the term 'construction of circle'?

A: Circle:  The circle is the set of points that are at equal distance from a given point. Construction…

Q: A_______ __________ is a positive angle whose vertex is at thecenter of a circle

A: It is given that, A_______ __________ is a positive angle whose vertex is at thecenter of a circle.

Q: What is the sum of the measures of the interior angles of an octagon?

A: The interior angle of a regular polygon is given by the expression . Here, is the interior angle of…

Q: Show that the points of the bisector of an angle are equidistant from its sides.

A:

Q: For a circle of radius r, a central angle of o degrees subtends an arc whose length s is s = re.…

A: Given: Radius of circle is r. Central angle is θ. Since 1°=π180radians, Then θ°=π180×θ radians

Q: Suppose that a circle is divided by points A, B, C, and D into four congruent arcs. What is the…

A: Let r be the radius of the circle. Since the arcs formed by the points A, B, C and D are congruent,…

Q: Two congruent intersecting circles B and D (not shown) have a line (segment) of centers BD and a…

A: The figure is drawn as shown in the figure with the give conditions.B and D are the centers of two…

Q: "find the number of sides for a regular polygon whose measure of each interior angle is 168

A:

Q: What is the relationship of two secants intersecting in the interior of a circle to the measures of…

A:

Q: Every quadrilateral can be inscribed in a circle. O True O False

A: Answer -  False

Q: Suppose that a circle is divided into three congruent arcs by points A, B, and C. What is the…

A: Since, we have been given that a circle is divided into three congruentarcs by points A, B and C.…

Q: A circle is inscribed in a polygon if each side of the polygon is tangent to the circle. true or…

A: If all the vertices of a polygon are on the circumference of a circle, the polygon is inscribed in a…

Q: 2. What is the measure of an exterior angle of a regular octagon?

A: We have given a regular octagon. We have to measure the exterior angle of a regular octagon.

Q: Do you agree that if two lines intersect at the center of the circle, then the lines intercept two…

A: Yes. When two lines intersect, they form two pairs of vertical angles. Pairs of non-adjacent angles…

Q: Prove that an exterior angle of a regular polygon is equal to the angle at the center?

A: Let us consider a regular n-polygon  We know that the sum of the exterior angles of a polygon is =…

Q: Write a complete proof to prove that the base angles of an isosceles trapezoid are congruent

A:

Q: What is the sum of the exterior angles of any polygon?

A: See attached file for a step by step explanation.

Q: When two parallel lines are cut by a transversal, the alternate exterior angles A) congruent.

A: Given that: Two parallel lines intersected by a transversal line.

Q: 1. When two chords of a circle are parallel, are the arcs they intercept be congruent? How about the…

A: Given that two chords of a circle are parallel and the arcs intercept the congruent. The arc that…

Q: Prove that a quadrilateral can be inscribed in a circle if and only if its opposite angles are…

A:

Q: If line DB is the perpendicular bisector of AC, list all the congruent segments

A:

Q: Is there an analog to the SSS triangle congruence theorem for quadrilaterals?

A: To show whether there is an analog to the SSS triangle congruence theorem for quadrilateral.

Q: It is an angle whose vertex is on a circle and whose sides contain chords of the circle?

A: I have provided the answer in step 2.

Q: what is the measure of an interior angle of a regular nonagon?

A:

Q: A cyclic quadrilateral is a quadrilateral whose vertices are on the circle. Are opposite angles of…

A: Given :- A cyclic quadrilateral is a quadrilateral whose vertices are on the circle

Q: Base angles are congruent in an isosceles trapezoid. O True False

A: In an isosceles trapezoid,  two non-parallel  sides are equal. So, the base angles are same as equal…

Q: Construct the three perpendicular bisectors of sides and then the circumscribed circle for obtuse…

A:

Q: Determine the measure of one exterior angle of a regular 20-sided polygon.

A: The measure of an exterior angle of a regular polygon with n sides is 360n°.

Q: A circumscribed circle can be found by first finding the point of concurrency of the three angle…

A: Circumscribes circle is a circle which passes through the vertices of a polygon.

Q: A quadrilaterial with exactly one pair of opposite sides parallel is classified as Trapezoid…

A: Given that : A quadrilateral with exactly one pair of opposite sides parallel is classified as

Q: When two chords of a circle are parallel, are the arcs they intercept be congruent? How about the…

A: Topic = Circle   Chords within a circle can be related many ways. Parallel chords in the same circle…

Q: Is there a regular polygon whose angle at the center is 7°30'?

A: We have given the central angle 7°30'. In terms of degrees, 7°30' = 7° + 0.5° = 7.5°. The central…

Q: In circle J with mZHJK = 46°, find the angle measure of minor arc HK . %3D

A: We have to find m Hk

Q: Paragraph proof with a picture, please

A: To prove: Congruent chords are located at the same distance from the center of a circle.