## Angle Bisector & Median Calculator

## FAQs

**What is the difference between angle bisector and median?** An angle bisector is a line that divides an angle into two equal angles, while a median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

**Is a median always an angle bisector?** No, a median is not always an angle bisector. A median bisects the opposite side of a triangle, whereas an angle bisector divides an angle into two equal angles.

**What is the difference between perpendicular bisector, angle bisector, median, and altitude?**

- Perpendicular Bisector: A line that is perpendicular to a segment and passes through its midpoint.
- Angle Bisector: A line that divides an angle into two equal angles.
- Median: A line segment that connects a vertex of a triangle to the midpoint of the opposite side.
- Altitude: A perpendicular line segment drawn from a vertex to the opposite side or its extension.

**What is the difference between angle bisector theorem and definition of angle bisector?** The angle bisector theorem states that in a triangle, the angle bisector divides the opposite side into segments proportional to the adjacent sides. The definition of an angle bisector is a line that divides an angle into two equal angles.

**Are the median and angle bisector the same in an isosceles triangle?** No, the median and angle bisector are not the same in an isosceles triangle. The median from the vertex angle of an isosceles triangle is also its altitude, but the angle bisector is different.

**Does median bisect 90 degrees?** No, a median does not necessarily bisect a 90-degree angle. It bisects the opposite side of a triangle, not the angles.

**What is the difference between perpendicular and angle bisector theorem?** The perpendicular bisector theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. The angle bisector theorem relates the lengths of segments created by an angle bisector in a triangle.

**What is the difference between median and altitude of a triangle?** A median is a line segment connecting a vertex to the midpoint of the opposite side. An altitude is a perpendicular line segment drawn from a vertex to the opposite side or its extension.

**What is the theorem of the median of a triangle?** Theorem: In a triangle, the three medians are concurrent (they intersect at a single point), and this point is called the centroid.

**Does a perpendicular bisector create a median?** No, a perpendicular bisector does not create a median. A perpendicular bisector is a line that divides a segment into two equal parts and is perpendicular to that segment.

**Does a median bisect a segment?** Yes, a median bisects the opposite side of a triangle, dividing it into two equal segments.

**Can the altitude and median be the same for a triangle?** Yes, in an isosceles triangle, the altitude from the vertex angle is also the median.

**Is the median always the same line as the perpendicular bisector?** No, the median and perpendicular bisector are generally different lines in a triangle.

**Is the median its angle bisector and altitude as well in an equilateral triangle?** Yes, in an equilateral triangle, each median is also an angle bisector and an altitude.

**What is the angle bisector theorem in simple words?** The angle bisector theorem states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the adjacent sides.

**What does the angle bisector theorem tell us?** The angle bisector theorem tells us about the relationship between the lengths of segments created by an angle bisector in a triangle.

**What is the explanation of the angle bisector theorem?** The angle bisector theorem explains that the angle bisector of a triangle divides the opposite side into segments whose lengths are proportional to the lengths of the adjacent sides.

**Can median be the angle bisector of a triangle?** Yes, in an isosceles triangle, the median from the vertex angle is also an angle bisector.

**Is the median of a triangle the same as the perpendicular bisector?** No, the median and perpendicular bisector are different concepts. The median connects a vertex to the midpoint of the opposite side, while the perpendicular bisector is a line that is perpendicular to a segment and passes through its midpoint.

**Can the median of a triangle also be the perpendicular bisector of the same triangle?** No, the median of a triangle and the perpendicular bisector are generally not the same line.

**Does the median bisect the hypotenuse?** Yes, in a right triangle, the median drawn from the right angle to the hypotenuse bisects the hypotenuse.

**Is median equal to 90 degrees?** No, a median is not equal to 90 degrees. A median is a line segment connecting a vertex to the midpoint of the opposite side.

**What ratio do medians bisect each other in?** Medians bisect each other in the ratio 2:1.

**How do you prove the angle bisector theorem?** The angle bisector theorem can be proven using similar triangles created by the angle bisector in a triangle.

**Is an angle bisector the same as a perpendicular bisector?** No, an angle bisector and a perpendicular bisector are different concepts. An angle bisector divides an angle into two equal parts, while a perpendicular bisector is a line that is perpendicular to a segment and passes through its midpoint.

**Are angle bisectors of two lines always perpendicular?** No, angle bisectors of two lines are not always perpendicular. They are perpendicular only if the two lines are parallel.

**What is the altitude, median, and bisector of a triangle?**

- Altitude: A perpendicular line segment drawn from a vertex to the opposite side or its extension.
- Median: A line segment connecting a vertex to the midpoint of the opposite side.
- Bisector: A line that divides an angle into two equal angles.

**Can a median and an altitude of an isosceles triangle be equal?** Yes, in an isosceles triangle, the median from the vertex angle is also the altitude.

**Is the median always greater than altitude?** No, the median is not always greater than the altitude. It depends on the specific triangle and its properties.

**What is the relation between median of a triangle and sides of a triangle?** The median of a triangle connects a vertex to the midpoint of the opposite side. It doesn’t have a fixed ratio with the sides, but in certain special cases, medians and sides can have interesting relationships.

**Is the median of a triangle perpendicular to the base?** No, the median of a triangle is not necessarily perpendicular to the base. It connects the vertex to the midpoint of the opposite side.

**How do you find the equation of a median of a triangle?** To find the equation of a median of a triangle, you need to determine the coordinates of the vertices and use the midpoint formula to find the midpoint of the opposite side. Then, you can find the equation of the line passing through the vertex and the midpoint.

**How do you construct the median and altitude of a triangle?** To construct a median of a triangle, draw a line segment from a vertex to the midpoint of the opposite side. To construct an altitude, draw a perpendicular line from a vertex to the opposite side or its extension.

**Does a median divide a triangle into two equal areas?** Yes, the medians of a triangle intersect at a point called the centroid, which divides each median into segments in a 2:1 ratio. This property also results in the medians dividing the triangle into six equal areas.

**Does a median divide the side in half?** Yes, a median divides the side opposite the vertex in half, creating two segments of equal length.

**Is altitude always 90 degrees?** Yes, an altitude is always drawn perpendicular to the base (opposite side) of the triangle, which makes it form a 90-degree angle.

**Can the three altitudes be three medians of a triangle?** No, the three altitudes cannot be three medians of a triangle. However, in an equilateral triangle, all three altitudes are also medians.

**Can a perpendicular bisector be an altitude of a triangle?** Yes, in an isosceles triangle, the perpendicular bisector of the base can also be considered an altitude.

**What if medians are perpendicular to each other?** If the medians of a triangle are perpendicular to each other, it indicates that the triangle is a right triangle.

**What is one similarity between perpendicular bisectors and medians?** Both perpendicular bisectors and medians of a triangle pass through a common point called the circumcenter and centroid, respectively.

**What is the concurrence of medians and altitudes?** The medians of a triangle intersect at a point called the centroid, while the altitudes intersect at a point called the orthocenter.

**Is the median the same as the angle bisector?** No, the median and angle bisector are different. The median connects a vertex to the midpoint of the opposite side, while the angle bisector divides an angle into two equal angles.

**What is the difference between a bisector and a median?** A bisector divides an angle or segment into two equal parts, while a median connects a vertex to the midpoint of the opposite side of a triangle.

**Are the median and angle bisector the same in an isosceles triangle?** No, in an isosceles triangle, the median from the vertex angle is not the same as the angle bisector.

**Can the altitude and median be the same for a triangle?** Yes, in an isosceles triangle, the altitude from the vertex angle is also the median.

**Does a perpendicular bisector create a median?** No, a perpendicular bisector does not create a median. It creates two segments of a segment, each equal in length.

**What if the median of a triangle is perpendicular and opposite side of a triangle is?** If the median of a triangle is perpendicular and opposite side is also perpendicular, it could imply that the triangle is a right triangle.

**Is a median of a triangle divides it into two equal areas?** Yes, the medians of a triangle divide it into six equal areas, not two. Each median divides the opposite side into segments in a 2:1 ratio.

**Are the median and altitude the same in an equilateral triangle?** No, in an equilateral triangle, the median and altitude are not the same. However, they have interesting relationships, such as intersecting at a point 1/3 of the way from the vertex to the base.

**Can a median of a triangle also be an angle bisector?** Yes, in an isosceles triangle, the median from the vertex angle is also an angle bisector.

**Does the median of a triangle always bisect the angle?** No, the median of a triangle does not bisect the angle. It connects a vertex to the midpoint of the opposite side.

**Does the median equal half the hypotenuse?** No, the median does not necessarily equal half the hypotenuse of a right triangle.

**What is the relation between median and hypotenuse of a right triangle?** The median of a right triangle is half the length of the hypotenuse.

**How to calculate the median?** To calculate the median of a triangle, find the midpoint of the opposite side and calculate the length of the line segment connecting the vertex to the midpoint.

**Is median always 50%?** Yes, the median divides the opposite side of a triangle into two segments in a 1:1 ratio, meaning each segment is 50% of the total length.

**What divides each median into a 2:1 ratio?** The centroid of a triangle divides each median into segments in a 2:1 ratio. The longer segment is twice as long as the shorter one.

**What ratio does median divide?** The medians of a triangle divide each other in a 2:1 ratio.

**What are the rules for the angle bisector theorem?** The angle bisector theorem states that the ratio of the lengths of segments created by an angle bisector in a triangle is proportional to the ratios of the lengths of the adjacent sides.

**Is bisector always 90 degrees?** No, a bisector is not always 90 degrees. A bisector divides an angle into two equal angles, but the angle bisector itself is not necessarily perpendicular to the sides.

**What is the difference between perpendicular and angle bisector theorem?** The perpendicular bisector theorem relates to the perpendicular bisector of a segment, stating that any point on the perpendicular bisector is equidistant from the endpoints of the segment. The angle bisector theorem deals with segments created by an angle bisector in a triangle.

**What is the difference between angle bisector and perpendicular lines?** An angle bisector divides an angle into two equal angles, while perpendicular lines form a 90-degree angle at their intersection.

**Is an angle bisector always perpendicular to the opposite side?** No, an angle bisector is not always perpendicular to the opposite side of the triangle. It only guarantees that it divides the angle into two equal angles.

**Is it possible for two lines to be perpendicular but not bisect each other?** Yes, it’s possible for two lines to be perpendicular but not bisect each other. For example, consider two lines that intersect at a point outside the line segment.

**How do you find the median and altitude of a triangle?** To find the median of a triangle, connect a vertex to the midpoint of the opposite side. To find the altitude, draw a perpendicular line from a vertex to the opposite side or its extension.

**How do you identify angle bisectors in a triangle from the altitude of a triangle?** Angle bisectors divide angles into two equal angles. Altitudes are perpendicular lines from a vertex to the opposite side. They are different concepts and can be identified based on their definitions.

**How to prove the median of an isosceles triangle as the altitude?** To prove that the median of an isosceles triangle is also the altitude, you can use the congruence between the two right triangles formed by the median and half of the base.

**What is the median, altitude, and angle bisector of a triangle?**

- Median: A line segment connecting a vertex to the midpoint of the opposite side.
- Altitude: A perpendicular line segment from a vertex to the opposite side.
- Angle Bisector: A line that divides an angle into two equal angles.

**Can a median and an altitude of an isosceles triangle be equal?** Yes, in an isosceles triangle, the median drawn from the vertex angle is also the altitude.

**Is the median always greater than altitude?** No, the median is not always greater than the altitude. It depends on the specific triangle and its properties.

**What is the relation between median of a triangle and sides of a triangle?** The median of a triangle connects a vertex to the midpoint of the opposite side. It doesn’t have a fixed ratio with the sides, but in certain special cases, medians and sides can have interesting relationships.

**Is the median of a triangle perpendicular to the base?** No, the median of a triangle is not necessarily perpendicular to the base. It connects the vertex to the midpoint of the opposite side.

**How do you find the equation of a median of a triangle?** To find the equation of a median of a triangle, you need to determine the coordinates of the vertices and use the midpoint formula to find the midpoint of the opposite side. Then, you can find the equation of the line passing through the vertex and the midpoint.

**How do you construct the median and altitude of a triangle?** To construct a median of a triangle, draw a line segment from a vertex to the midpoint of the opposite side. To construct an altitude, draw a perpendicular line from a vertex to the opposite side or its extension.

**Does a median divide a triangle into two equal areas?** Yes, the medians of a triangle intersect at a point called the centroid, which divides each median into segments in a 2:1 ratio. This property also results in the medians dividing the triangle into six equal areas.

**Does a median divide the side in half?** Yes, a median divides the side opposite the vertex in half, creating two segments of equal length.

**Is altitude always 90 degrees?** Yes, an altitude is always drawn perpendicular to the base (opposite side) of the triangle, which makes it form a 90-degree angle.

**Can the three altitudes be three medians of a triangle?** No, the three altitudes cannot be three medians of a triangle. However, in an equilateral triangle, all three altitudes are also medians.

**Can a perpendicular bisector be an altitude of a triangle?** Yes, in an isosceles triangle, the perpendicular bisector of the base can also be considered an altitude.

**What if medians are perpendicular to each other?** If the medians of a triangle are perpendicular to each other, it indicates that the triangle is a right triangle.

**What is one similarity between perpendicular bisectors and medians?** Both perpendicular bisectors and medians of a triangle pass through a common point called the circumcenter and centroid, respectively.

**What is the concurrence of medians and altitudes?** The medians of a triangle intersect at a point called the centroid, while the altitudes intersect at a point called the orthocenter.

**Is the median the same as the angle bisector?** No, the median and angle bisector are different. The median connects a vertex to the midpoint of the opposite side, while the angle bisector divides an angle into two equal angles.

**What is the difference between a bisector and a median?** A bisector divides an angle or segment into two equal parts, while a median connects a vertex to the midpoint of the opposite side of a triangle.

**Are the median and angle bisector the same in an isosceles triangle?** No, in an isosceles triangle, the median from the vertex angle is not the same as the angle bisector.

**Can the altitude and median be the same for a triangle?** Yes, in an isosceles triangle, the altitude from the vertex angle is also the median.

**Does a perpendicular bisector create a median?** No, a perpendicular bisector does not create a median. It creates two segments of a segment, each equal in length.

**What if the median of a triangle is perpendicular and opposite side of a triangle is?** If the median of a triangle is perpendicular and opposite side is also perpendicular, it could imply that the triangle is a right triangle.

**Is a median of a triangle divides it into two equal areas?** Yes, the medians of a triangle divide it into six equal areas, not two. Each median divides the opposite side into segments in a 2:1 ratio.

**Are the median and altitude the same in an equilateral triangle?** No, in an equilateral triangle, the median and altitude are not the same. However, they have interesting relationships, such as intersecting at a point 1/3 of the way from the vertex to the base.

**Can a median of a triangle also be an angle bisector?** Yes, in an isosceles triangle, the median from the vertex angle is also an angle bisector.

**Does the median of a triangle always bisect the angle?** No, the median of a triangle does not bisect the angle. It connects a vertex to the midpoint of the opposite side.

**Does the median equal half the hypotenuse?** No, the median does not necessarily equal half the hypotenuse of a right triangle.

**What is the relation between median and hypotenuse of a right triangle?** The median of a right triangle is half the length of the hypotenuse.

**How to calculate the median?** To calculate the median of a triangle, find the midpoint of the opposite side and calculate the length of the line segment connecting the vertex to the midpoint.

**Is median always 50%?** Yes, the median divides the opposite side of a triangle into two segments in a 1:1 ratio, meaning each segment is 50% of the total length.

**What divides each median into a 2:1 ratio?** The centroid of a triangle divides each median into segments in a 2:1 ratio. The longer segment is twice as long as the shorter one.

**What ratio does median divide?** The medians of a triangle divide each other in a 2:1 ratio.

**What are the rules for the angle bisector theorem?** The angle bisector theorem states that the ratio of the lengths of segments created by an angle bisector in a triangle is proportional to the ratios of the lengths of the adjacent sides.

**Is bisector always 90 degrees?** No, a bisector is not always 90 degrees. A bisector divides an angle into two equal angles, but the angle bisector itself is not necessarily perpendicular to the sides.

**What is the difference between perpendicular and angle bisector theorem?** The perpendicular bisector theorem relates to the perpendicular bisector of a segment, stating that any point on the perpendicular bisector is equidistant from the endpoints of the segment. The angle bisector theorem deals with segments created by an angle bisector in a triangle.

**What is the difference between angle bisector and perpendicular lines?** An angle bisector divides an angle into two equal angles, while perpendicular lines form a 90-degree angle at their intersection.

**Is an angle bisector always perpendicular to the opposite side?** No, an angle bisector is not always perpendicular to the opposite side of the triangle. It only guarantees that it divides the angle into two equal angles.

**Is it possible for two lines to be perpendicular but not bisect each other?** Yes, it’s possible for two lines to be perpendicular but not bisect each other. For example, consider two lines that intersect at a point outside the line segment.

**How do you find the median and altitude of a triangle?** To find the median of a triangle, connect a vertex to the midpoint of the opposite side. To find the altitude, draw a perpendicular line from a vertex to the opposite side or its extension.

**How do you identify angle bisectors in a triangle from the altitude of a triangle?** Angle bisectors divide angles into two equal angles. Altitudes are perpendicular lines from a vertex to the opposite side. They are different concepts and can be identified based on their definitions.

**How to prove the median of an isosceles triangle as the altitude?** To prove that the median of an isosceles triangle is also the altitude, you can use the congruence between the two right triangles formed by the median and half of the base.

**What is the median, altitude, and angle bisector of a triangle?**

- Median: A line segment connecting a vertex to the midpoint of the opposite side.
- Altitude: A perpendicular line segment from a vertex to the opposite side.
- Angle Bisector: A line that divides an angle into two equal angles.

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