Class 9 Theorems Flashcards
what is a ray?
a line that has a fixed starting point but no endpoint.
Since a ray has no end point, it can’t be measured.
what is vertex?
the point where two lines meet to form an angle
what is right bisector?
a line bisector that is perpendicular to the line it is bisecting.
it creates 2 congruent right angles.
aka Perpendicular Bisector
what is line bisector?
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.
what is angle bisector?
a line or ray that passes through the vertex of an angle that divides the angle into two congruent angles.
what are supplementary & complementary angles?
those angles that sum up to 180 degrees.
those angles that sum up to 90 degrees.
what does concurrent mean?
3 or more lines meeting at same point.
In a parallelogram:
opposite sides are congruent.
opposite angles are congruent.
the diagonals bisect each other.
if 2 opposite sides of a quadrilateral are congruent & parallel, it is a ______________.
parallelogram
what is a median?
a line segment that joins a vertex to the mid-point of opposite sides.
angles opposite to congruent sides are ____________.
also congruent.
Isosceles Triangle Theorem. The Isosceles Triangle Theorem states that the angles opposite congruent sides of a triangle are also congruent.
what is corollary?
statement that follows naturally from some other statement that has been proven.
what is an equiangular triangle?
equal sides & equal angles.
each angle of an equiangular triangle is equal to 60°.
what are vertical angles?
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.
what are adjacent angles?
adjacent angles lie exactly next to each other.
They’re not always congruent.
are adjacent angles always supplementary?
no
they have to share a common side and vertex.
Adjacent angles might be supplementary, but they could be complementary as well.
what is the sum of interior angles of parallel lines?
180°
FMIGTN
What is altitude in a triangle?
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
if △ABC is equilaterial, then what is value of ∠B?
60 degrees
the 3 angles of the equilateral triangle are congruent & equal to 60° .
the right bisectors of the sides of a triangle is _________.
concurrent
the side opposite to greater angle is longer than side of smaller angle. T/F
T
what are non-adjacent angles?
angles that are not adjacent or lie next or neighbour each other.
an exterior angle of a triangle is greater than _______________.
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.
from a point outside a line, _________ is the shortest distance from the point to the line.
perpendicular
