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9th mathematics Chapter12 Line bisectors and angle bisectors

Sr #QuestionsABCD
1

What is the definition of a bisector in geometry?

 A line that divides an angle into two congruent angles A line that divides a segment into two equal parts A line that bisects both angles and segments A line that is perpendicular to another line
2

The angle bisector of an angle divides the opposite side into segments that are:

 Congruent Proportional Equal None of the above
3

The point where the perpendicular bisectors of the sides of a triangle intersect is called the:

 Incenter Circumcenter Centroid Orthocenter
4

What is the exterior angle bisector of an angle?

 A line that bisects the angle internally A line that bisects the angle externally A line that extends the angle to form two supplementary angles A line that is perpendicular to the angle
5

What is the angle bisector of a straight angle?

 A point A line segment A line None of the above
6

The angle bisector of an equilateral triangle is also its:

 Perpendicular bisector Median Altitude Incenter
7

The point of concurrency of the angle bisectors in a triangle is called the:

 Incenter Centroid Circumcenter Orthocenter
8

If the angle bisector of an angle in a triangle is also the median, the triangle is:

 Acute-angled Obtuse-angled Right-angled Equilateral
9

If a line bisects an angle and is also perpendicular to the opposite side, it is the:

 Perpendicular bisector Angle bisector Median Altitude
10

In a triangle, the angle bisector is the same as:

 Perpendicular bisector Median Altitude None of the above
11

In an isosceles triangle, the angle bisector of the vertex angle is also the:

 Altitude Median Perpendicular bisector None of the above
12

In a triangle, the angle bisectors meet at the:

 Incenter Circumcenter Centroid Orthocenter
13

What is the relationship between the incenter and the circumcenter of a triangle?

 They are always the same point. They are always different points. They coincide only in equilateral triangles. Their relationship depends on the type of triangle.
14

The incenter of a triangle is equidistant from:

 The vertices of the triangle The midpoints of the sides of the triangle The intersection points of angle bisectors The circumcenter of the triangle
15

If a line bisects a segment at a right angle, it is called a:

 Perpendicular bisector Median Altitude Angle bisector
16

What is the angle bisector theorem?

 The bisector of an angle in a triangle divides the opposite side in the ratio of the other two sides. The bisector of an angle in a triangle divides the opposite side proportionally to the adjacent sides. The bisector of an angle in a triangle is always equal to half of the angle. The bisector of an angle in a triangle bisects the opposite side.
17

The incenter of an equilateral triangle is also its:

 Circumcenter Centroid Orthocenter None of the above
18

The perpendicular bisector of a segment passes through its:

 Midpoint Endpoint Center Opposite endpoint
19

What is the exterior angle bisector theorem?

 The exterior angle bisector of a triangle is always equal to half of the exterior angle. The exterior angle bisector of a triangle divides the opposite side proportionally to the adjacent sides. The exterior angle bisector of a triangle divides the opposite side in the ratio of the other two sides. The exterior angle bisector of a triangle is perpendicular to the interior angle bisector.
20

In a right-angled triangle, the angle bisector of the right angle is also the:

 Median Altitude Perpendicular bisector Hypotenuse
21

If a line bisects an angle, the two resulting angles are:

 Congruent Supplementary Complementary Vertical angles
22

If a line bisects a segment, the two resulting segments are:

 Congruent Proportional Perpendicular Supplementary
23

If the angle bisector of an angle in a triangle is also the altitude, the triangle is:

 Acute-angled Obtuse-angled Right-angled Equilateral
24

The angle bisector of an isosceles triangle divides the base into segments that are:

 Equal Congruent Proportional Perpendicular
25

In a triangle, the angle bisector divides the opposite side into two segments in the ratio of:

 1:1 2:1 1:2 1:3