isosceles triangle and triangle inequalities Flashcards
the sum of the lengths of any
two sides of a triangle is greater
than the length of the third side.
triangle inequality theorem
If one angle is larger than the
other angles, the side opposite
the larger angle is the longest
side
unequal angle theorem
If one side is larger than the other
side, the side opposite the longest side is the largest angle.
unequal side theorem
What does the sum of any two lengths of a triangle have to do with its third length in identifying if the given lengths can be possibly made into a triangle?
In identifying if the given lengths can be possibly made into a triangle, it must follow that the sum of any two lengths of a triangle must be greater than
its third side.
How can you measure the possible length of the third side of the triangle given its two lengths?
Finding the possible length of the third side of a triangle is through subtracting and adding the given
two lengths. Additionally, its possible length must be greater than the difference of the given two lengths but less than its sum.
For any triangle, the measure of
an exterior angle is equal to the
sum of the measure of its two remote interior angles.
exterior angle theorem
states that if two angles form a linear pair, then the two angles are supplementary and adjacent.
linear pair theorem
is an angle that forms a linear pair with one of the interior angles of a triangle.
exterior angle
is an angle of triangle that is
not adjacent to a
specified exterior angles.
remote interior angle
If two sides of a triangle are
congruent, then the angles
opposite to those sides are congruent.
isosceles triangle theorem
PARTS OF AN ISOSCELES TRIANGLE
vertex, base, base angles, and legs
If two sides of a triangle are
equal, then the angles opposite to these sides are equal.
base angle theorem
The degree measure of an exterior angle of a triangle is greater than the degree measure of either of its remote interior angles.
exterior angle inequality theorem
the measure of an
exterior angle is equal to the sum of its two remote interior angles.
exterior angle theorem
What inequality can be formed when an exterior angle is compared to either of its remote interior angles?
By Exterior Angle Inequality Theorem, the inequality that can be formed when an exterior angle is compared to either of its remote interior angles is that, the measure of an exterior angle is greater than to either of its remote interior angles.
