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23 Cards in this Set
- Front
- Back
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what is a median?
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it connects a vertex of a triangle to the midpoint of the opp. side
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what is an angle bisector?
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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
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how many angle bisectors can a triangle have?
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3 because a triangle has 3 sides
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what is an altitude?
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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.
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what are the steps for writing indirect proof?
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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. |
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what is the definition of inequality?
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for any real numbers a and b, a>b if there is a positive c such that a=b+c
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LL theorem uses:
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SAS
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HA theorem uses:
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AAS
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LA theorem uses:
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ASA and SAA
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HL is a:
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postulate because you need SSA to prove it and SSA is a postulate
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what is the inequality theorem say?
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a+b>c
a+c>b b+c>a |
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what does the hinge theorem say?
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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.
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what does the SSS inequality say?
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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.
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hinge theorem is aka:
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SAS inequality theorem
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the perpendicular segment from a point to a plane is the shortest segment from the point to the plane
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the
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the perpendicular segment from a point to a line is the shortest segment from the point to the line
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the
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if one < of a tri. is greater than another <, then the side opp. the greater < is longer than the side opp. the lesser <.
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converse of 5-9
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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
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converse of 5-10
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what is a perp. bisector?
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a line or line segment that passes thru the midpoint of a side of a triangle AND is perp. to that side
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a point on the perp. bisector of a segment is equidistant from the endpoints of the segment
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a point
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a point equidistant from the endpoints of a segment lies on the perp. bisector of the segment
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a point
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a point on the bisector of an < is equidistant from the sides of the <.
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a point
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a point in the interior of or on an < and equidistant from the sides of an < lies on the bisector of the <.
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a point
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