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this can be proved by drawing the given circle

now x=2a and x=2b (angle at the centre is double the angle at any point on the circumference.

therefore. 2a=2b

hence. a=b

as asked. this theorem is proved..

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An angle with its vertex and endpoints on the circle?

If the vertex is at the centre of the circle then this forms a sector of the circle.If the two endpoints and the vertex form an angle in a segment, then the vertex can be at any point on the circle within the same segment and all angles so formed are equal.


Is a segment the same thing as an angle?

No, a segment is a piece of a line. However, two segments that intersect at a point make an angle. In fact, the segments that make up the angle are called the sides of the angle.


What statement describes the points on the perpendicular bisector?

The points on the perpendicular bisector of a segment are equidistant from the segment's endpoints. This means that if you take any point on the perpendicular bisector, it will be the same distance from both endpoints of the segment. Additionally, the perpendicular bisector is a line that divides the segment into two equal parts at a right angle.


Why are the median angle bisector and altitude from the vertex angle of an isoceles triangle all the same?

It's in the definition of an angle bisector: An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.and an isoceles triangle:it is a triangle with (at least) two equal sides. This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.


How can you prove segments are equal?

To prove that segments are equal, you can use various methods, such as the Segment Addition Postulate, which states that if two segments are composed of the same subsegments, they are equal. Additionally, you can employ the properties of congruence, such as the Reflexive Property (a segment is equal to itself), or the Transitive Property (if segment AB is equal to segment CD, and segment CD is equal to segment EF, then segment AB is equal to segment EF). Geometric constructions and the use of measurement tools can also provide empirical evidence of equal lengths.

Related Questions

An angle with its vertex and endpoints on the circle?

If the vertex is at the centre of the circle then this forms a sector of the circle.If the two endpoints and the vertex form an angle in a segment, then the vertex can be at any point on the circle within the same segment and all angles so formed are equal.


Is a segment the same thing as an angle?

No, a segment is a piece of a line. However, two segments that intersect at a point make an angle. In fact, the segments that make up the angle are called the sides of the angle.


Why are the median angle bisector and altitude from the vertex angle of an isoceles triangle all the same?

It's in the definition of an angle bisector: An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.and an isoceles triangle:it is a triangle with (at least) two equal sides. This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.


What is the measurement of a congruent angle?

A congruent angle can also mean equal angle. So there is no set measurement of a congruent angle. Just the same as the angle it is equal to.


What is the meaning of congruent segment?

Congruent Segment If They Have the same or equal Measures.. posted by: ritzjohn_41@yahoo.com


How can you prove segments are equal?

To prove that segments are equal, you can use various methods, such as the Segment Addition Postulate, which states that if two segments are composed of the same subsegments, they are equal. Additionally, you can employ the properties of congruence, such as the Reflexive Property (a segment is equal to itself), or the Transitive Property (if segment AB is equal to segment CD, and segment CD is equal to segment EF, then segment AB is equal to segment EF). Geometric constructions and the use of measurement tools can also provide empirical evidence of equal lengths.


If two angle have the same angle measures then they are said to be?

They are equal angles.


Does a full angle can be called a circle?

No. A full angle is a segment of a line which goes to a vertex and returns along the same path. Any point on the line segment, other than the vertex, will trace out a circle but the angle itself is NOT a circle.


How do the Triangle-Angle Bisector Theorem and the Angle Bisector Theorem differ?

They are the same concept, one for the angle and 1 for triangle.Definition of a triangle angle bisector is a line segment that bisects one of the vertex angles of a triangle.Definition of an angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.


Supplements of the same angle are congruent what's the best statement for reason 6 of this proof?

angle B and angle D are supplements, angle B is congruent to angle D, angle A is congruent to angle A, or angle A is congruent to angle C


Is this true If a median an altitude and an angle bisector are the same segment in a triangle the triangle is scalene?

No, it's not true.


What are all the characteristics of a perpendicular bisector?

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle. It has two key characteristics: it is equidistant from the endpoints of the segment it bisects, meaning any point on the bisector is the same distance from both endpoints, and it intersects the segment at its midpoint. Additionally, the slope of the perpendicular bisector is the negative reciprocal of the slope of the original segment.