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24 Cards in this Set
- Front
- Back
What 4 Theorems can be used to prove 2 right triangles are congruent?
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LL (leg, leg)
HA (hypotenuse, acute angle) LA (leg, acute angle) HL (hypotenuse, leg) |
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What is the LL theorem?
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If the legs of one RIGHT triangle are congruent to the legs of another RIGHT triangle, then the triangles are congruent.
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What is the HA theorem?
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If hypotenuse and an acute angle of one RIGHT triangle are congruent to the hypotenuse and corresponding acute angle of another RIGHT triangle, then the two triangles are congruent.
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What is the LA theorem?
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If one leg and an acute angle of one RIGHT triangle are congruent to the corresponding leg and acute angle of another RIGHT triangle, then the two triangles are congruent.
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What is the HL Theorem?
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If the hypotenuse and a leg of one RIGHT triangle are congruent to the hypotenuse and corresponding leg of another RIGHT triangle, then the triangles are congruent.
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What is a perpendicular bisector in a triangle?
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A line that passes through the MIDPOINT of a side of a triangle and is PERPENDICULAR to that side.
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What is a perpendicular bisector?
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A line that passes through the midpoint of a side of a triangle and is perpendicular to that side.
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What is the perpendicular bisector theorem?
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If you draw 3 perpendicular bisectors in the same triangle what is the name of the point where they intersect?
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Circumcenter
Point P is the circumcenter - and is the intersection of the perpendicular bisectors |
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The circumcenter is equidistant to what point on the circle?
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The 3 lines from the circumcenter to the vertices of the triangle are equidistant (equal).
PB = PA = PC |
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What is an Angle Bisector in a triangle?
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A segment that bisects (cuts in half) an angle of a triangle has one endpoint at a vertex of the triangle, and the other endpoint at another point on the triangle.
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What is the angle bisector theorem?
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If the 3 angles bisectors are drawn in a triangle what is the name of their point of intersection?
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Incenter
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The incenter is equidistant from what part of the triangle?
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It is equidistant from the sides of the triangle.
PD = PE = PF |
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What is a Median of a triangle?
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A segment that connects a VERTEX of a triangle to the MIDPOINT of the opposite side.
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If we draw 3 medians in a triangle what is the name of their point of intersection?
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Centroid
P is the centroid of the triangle |
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How are the lengths of the segments from the centroid related?
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The segment from the vertex to the centroid = 2/3 times the entire length of the median
AP = 2/3(AK) BP = 2/3(BL) CP = 2/3(CJ) |
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What is the Altitude of a triangle?
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A segment from a vertex of a triangle to the line containing the opposite side and perpendicular to the line containing the side.
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If the 3 altitudes are drawn in a triangle what is the name of their point of intersection?
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Orthocenter
P is the orthocenter of triangle ABC |
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What is the definition of concurrent lines?
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Three or more lines that intersect at a common point.
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What is the definition of a point of concurrency?
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The point of intersection of concurrent lines.
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What is the triangle inequality theorem?
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Use the hinge theorem (SAS inequality) to compare side BC and GH of the triangles.
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Because two sides are equal and the measure of angle A is greater than measure of angle F then:
BC > GH (BC is greater than GH) |
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Use the hinge theorem (SSS inequality) to compare angle R and angle L.
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If 2 sides are congruent and PQ is smaller than JK then:
measure of angle PRQ > measure of angle JLK |