Class 9 Theorems

Question 1

what is a ray?

Answer 1

a line that has a fixed starting point but no endpoint.

Since a ray has no end point, it can’t be measured.

Question 2

what is vertex?

Answer 2

the point where two lines meet to form an angle

Question 3

what is right bisector?

Answer 3

a line bisector that is perpendicular to the line it is bisecting.

it creates 2 congruent right angles.

aka Perpendicular Bisector

Question 4

what is line bisector?

Answer 4

a line that divides another line segment into two equal parts.

it is equidistant from the two endpoints of the original line segment.

it passes through midpoint of line sgement.

Question 5

what is angle bisector?

Answer 5

a line or ray that passes through the vertex of an angle that divides the angle into two congruent angles.

Question 6

what are supplementary & complementary angles?

Answer 6

those angles that sum up to 180 degrees.
those angles that sum up to 90 degrees.

Question 7

what does concurrent mean?

Answer 7

3 or more lines meeting at same point.

Question 8

In a parallelogram:

Answer 8

opposite sides are congruent.
opposite angles are congruent.
the diagonals bisect each other.

Question 9

if 2 opposite sides of a quadrilateral are congruent & parallel, it is a ______________.

Answer 9

parallelogram

Question 10

what is a median?

Answer 10

a line segment that joins a vertex to the mid-point of opposite sides.

Question 11

angles opposite to congruent sides are ____________.

Answer 11

also congruent.

Isosceles Triangle Theorem. The Isosceles Triangle Theorem states that the angles opposite congruent sides of a triangle are also congruent.

Question 12

what is corollary?

Answer 12

statement that follows naturally from some other statement that has been proven.

Question 13

what is an equiangular triangle?

Answer 13

equal sides & equal angles.
each angle of an equiangular triangle is equal to 60°.

Question 14

what are vertical angles?

Answer 14

the angles that lie opposite to each other when two lines intersect.
Two vertical angles always share a common vertex.

Vertical angles are always congruent.

Question 15

what are adjacent angles?

Answer 15

adjacent angles lie exactly next to each other.
They’re not always congruent.

Question 16

are adjacent angles always supplementary?

Answer 16

no
they have to share a common side and vertex.
Adjacent angles might be supplementary, but they could be complementary as well.

Question 17

what is the sum of interior angles of parallel lines?

Answer 17

180°

FMIGTN

Question 18

What is altitude in a triangle?

Answer 18

The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.
The altitude makes a right-angle triangle with the base.

aka the height of the triangle

Question 19

if △ABC is equilaterial, then what is value of ∠B?

Answer 19

60 degrees

the 3 angles of the equilateral triangle are congruent & equal to 60° .

Question 20

the right bisectors of the sides of a triangle is _________.

Answer 20

concurrent

Question 21

the side opposite to greater angle is longer than side of smaller angle. T/F

Answer 21

T

Question 22

what are non-adjacent angles?

Answer 22

angles that are not adjacent or lie next or neighbour each other.

Question 23

an exterior angle of a triangle is greater than _______________.

Answer 23

non-adjacent interior angle.

the measure of an exterior angle = the sum of its 2 non-adjacent interior angles.
the exterior angle is also greater than either of the individual non-adjacent interior angles.

Question 24

from a point outside a line, _________ is the shortest distance from the point to the line.

Answer 24

perpendicular