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23 Cards in this Set

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  • Back
what is a median?
it connects a vertex of a triangle to the midpoint of the opp. side
what is an angle bisector?
it is a segment that bisects an angle of the traingle and has one endpoint at a vertex of the triangle and the endpoint at another point on the triangle
how many angle bisectors can a triangle have?
3 because a triangle has 3 sides
what is an altitude?
has an endpoint at a vertex of a triangle and the other on the line that contains the side opp. that vertex so that the segment is perp. to this line.
what are the steps for writing indirect proof?
1.assume that the conclusion is false.
2.show that the assumption leads to a contradiction of the hypothesis or some other fact such as a postulate, theorem, or corollary.
3.point out that the assumption must be false, and therefore, the conclusion must be true.
what is the definition of inequality?
for any real numbers a and b, a>b if there is a positive c such that a=b+c
LL theorem uses:
SAS
HA theorem uses:
AAS
LA theorem uses:
ASA and SAA
HL is a:
postulate because you need SSA to prove it and SSA is a postulate
what is the inequality theorem say?
a+b>c
a+c>b
b+c>a
what does the hinge theorem say?
if 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angle in one triangle is greater than the included < in the other, then the 3rd side of the first tri. is longer than the 3rd side in the second tri.
what does the SSS inequality say?
if 2 sides of one tri. are congruent to 2 sides of another tri. nd the third side in one tri. is longer than the 3rd side in the other, then the < btwn the pair of congruent sides in the first tri. is > than the corres. included < in the second tri.
hinge theorem is aka:
SAS inequality theorem
the perpendicular segment from a point to a plane is the shortest segment from the point to the plane
the
the perpendicular segment from a point to a line is the shortest segment from the point to the line
the
if one < of a tri. is greater than another <, then the side opp. the greater < is longer than the side opp. the lesser <.
converse of 5-9
if one side of a tri. is longer than another side, then the < opp. the longer side is greater than the < opp. the shorter side
converse of 5-10
what is a perp. bisector?
a line or line segment that passes thru the midpoint of a side of a triangle AND is perp. to that side
a point on the perp. bisector of a segment is equidistant from the endpoints of the segment
a point
a point equidistant from the endpoints of a segment lies on the perp. bisector of the segment
a point
a point on the bisector of an < is equidistant from the sides of the <.
a point
a point in the interior of or on an < and equidistant from the sides of an < lies on the bisector of the <.
a point