Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
31 Cards in this Set
- Front
- Back
- 3rd side (hint)
|
Perpendicular bisector |
A point lies on the ________________ if and only if it is equidistant from both endpoints |
|
|
|
Circumcenter |
The perpendicular bisectors of a triangle meet up to form the _______________ |
|
|
|
Vertices |
The circumcenter is equidistant from ____________ |
|
|
|
Circumcenter and vertices |
The circumscribed circle uses what two points to make up its radii |
|
|
|
Altitude |
A segment that extends from a vertex and is perpendicular to the opposite side |
|
|
|
Orthocenter (Orthocenter theorem) |
Lines that contain the altitudes of a triangle are concurrent at the ____________ |
|
|
|
Angle bisector |
A point lies on the ______________ if and only if it is equidistant from its sides |
|
|
|
Incenter (Incenter theorem) |
The triangle angle bisectors are concurrent at the |
|
|
|
Incenter |
Point that is equidistant from each side |
|
|
|
Inscribed circle |
The circle that has the radii that extends from the Incenter to the sides |
|
|
|
Median |
A segment that extends from a vertex to the midpoint of the opposite side |
|
|
|
Centroid |
The intersections of the medians |
|
|
|
Two-thirds of the distance |
The centroid is _________ from each vertex to the opposite sides midpoint |
|
|
|
Addition |
If a>b and c>_d then a+c>b+d |
|
|
|
Multiplicative |
If a>b and c>0 then ac>bc. If a>b and c<0 then ac |
|
|
|
Transitive |
If a>b and b>c then a>c |
|
|
|
Trichotomy |
A=b, a>b, or a |
|
|
|
Comparison Property |
For any real numbers a,b, and c, if a=b+c and c>0 then a>b |
|
|
|
Exterior angle inequality theorem |
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle |
|
|
|
Greater angle theorem |
If two sides of a triangle are not congruent the larger angle is opposite of the longer side |
|
|
|
Longer side theorem |
If two angles of a triangle are not congruent the longer side is opposite the larger angle |
|
|
|
Longest |
The hypotenuse is the _________ side in a right triangle |
|
|
|
Perpendicular segment |
The shortest segment from a point to a line is a ____________ |
|
|
|
Indirect proof |
In ___________ the statement and the negation are the only possibilities |
In ___________ the statement and the negation are the only possibilities |
|
|
Modus ponens |
P—> Q ; p therefore q |
|
|
|
Modus Tollens |
p—> q; ~p therefore ~q |
|
|
|
Then you are a US resident |
Where is the conclusion: If you live in Virginia, then you are a US Resident |
|
|
|
Law of Contradiction |
If an assumption leads to a contradiction then the assumption is false and its negation is true |
|
|
|
Triangle Inequality Theorem |
The sum of the lengths of any two sides of a triangle is greater than the length of the third side |
|
|
|
Third side of the first triangle is longer than the second (Hinge Theorem) |
If two sides of a triangle are congruent to two sides of a second triangle and the first angle is larger than the second then the |
|
|
|
The angle opposite of the third side of the first triangle is larger (Converse of the Hinge Theorem) |
If two sides of one triangle are congruent to two sides of a second triangle and the third side of the first is longer then the second then |
|
