Geometry Chapter 13 Flashcards
The largest angle of a triangle is opposite
the longest side.
The perpendicular from a point to a line
is the shortest segment from the point to the line.
If unequals are multiplied by the same negative number
the results are unequal in the opposite order.
If unequals are divided by the same negative number
the results are unequal in the opposite order.
The sum of the lengths of two sides of a triangle
is greater than the length of the third side.
If two sides of a triangle are congruent to two sides of another triangle
the triangle having the greater included angle has the greater third side.
In the same or equal circles, the greater arc has
the greater central angle.
The whole is greater than
any of its parts
The length of a line segment is the
shortest distance between two points
The length of the longest side of a triangle
is less than the sum of the lengths of the other two sides and greater than their difference.
If unequals are added to unequals of the same order
the sums are unequal in the same order
Since 5>3 and 4>1, we have 5+4>3+1 (or 9>4). If 2x-4
If the measures of two angles of a triangle are unequal
the lengths of the sides opposite these angles are unequal, the longer side being opposite the larger angle.
If the lengths of two sides of a triangle are unequal
the measures of the angles opposite these sides are unequal, the larger angle being opposite the longer side.
If two sides of a triangle are congruent to two sides of another triangle
the triangle having the greater third side has the greater angle opposite this side.
In the same or equal circles, the greater chord
has the greater minor arc
If unequals are subtracted from equals,
the differences are unequal in the opposite order.
Since 10=10 and 5>3, we have 10-5<10-3 (or 5<7). If x+y=12 and y>5, then x+y-y<12-5 or x<7.
In the same or equal circles, the greater central angle
has the greater arc.
In the same or equal circles, the chord at the smaller distance from the center
is the greater chord.
If equals are added to unequals
the sums are unequal in the same order
since 5>4 and 4=4, we know that 5+4>4+4 (or 9>8). If x-4+4
A quantity may be substituted for its equal
in any inequality.
If x>y and y=10, then x>10
The longest side of a triangle is opposite
the largest angle.
In a triangle, the measure of an exterior angle is
larger than the measure of either nonadjacent interior angle.
If equals are subtracted from unequals
the differences are unequal in the same order
Since 10>5 and 3=3, we have 10-3>5-3 (or 7>2). If x+6
If unequals are divided by the same positive number
the results are unequal in the same order.
In the same or equal circles, the greater chord is
at a smaller distance from the center.
If unequals are multiplied by the same positive number
the products are unequal in the same order.
If the first of three quantities is greater than the second and the second is greater than the third
then the first is greater than the third.
If x>y and y>z, then x>z
In the same or equal circles, the greater minor arc has
the greater chord
