# data[].attributes.body
If 2 sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side

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If 2 sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle

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The sum of the lengths of any two sides of a triangle is greater than the length of the third side

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If 2 angles of a triangle are not congruent, then the longer side lies opposite the larger angle

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If 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side

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Corollary to the Triangle Exterior Angle Theorem (5-9)

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Corollary to the Triangle Exterior Angle Theorem (5-9)

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The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles

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If a = b + c and c > 0, then a > b

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indirect proof: a proof involving indirect reasoning

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indirect proof: a proof involving indirect reasoning

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indirect reasoning: all possibilities are considered and then all but one are proved false so the remaining possibility must be true

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indirect reasoning: all possibilities are considered and then all but one are proved false so the remaining possibility must be true

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inscribed in: when a circle is drawn inside of a triangle

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inscribed in: when a circle is drawn inside of a triangle

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incenter of the triangle: the point of concurrency of the angle bisectors of a triangle 

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incenter of the triangle: the point of concurrency of the angle bisectors of a triangle 

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Concurrency of Angle Bisectors Theorem (5-7)

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Concurrency of Angle Bisectors Theorem (5-7)

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The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle

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it can be inside an acute triangle, on a right triangle, and outside an obtuse triangle

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circumscribed about: when one draws a circle around the triangle

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circumscribed about: when one draws a circle around the triangle

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circumcenter of the triangle: the point of concurrency of the PERPENDICULAR BISECTORS of a triangle

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circumcenter of the triangle: the point of concurrency of the PERPENDICULAR BISECTORS of a triangle

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Concurrency of Perpendicular Bisectors Theorem (5-6)

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Concurrency of Perpendicular Bisectors Theorem (5-6)

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The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices

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point of concurrency: the point in which 3 or more (concurrent) lines intersect 

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point of concurrency: the point in which 3 or more (concurrent) lines intersect 

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concurrent: when 3 or more lines intersect at one point

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concurrent: when 3 or more lines intersect at one point

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Converse of the Angle Bisector Theorem (5-5)

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Converse of the Angle Bisector Theorem (5-5)

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If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector

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If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle

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distance from a point to a line: the length of the perpendicular segment from the point to the line

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distance from a point to a line: the length of the perpendicular segment from the point to the line

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Converse of the Perpendicular Bisector Theorem (5-3)

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Converse of the Perpendicular Bisector Theorem (5-3)

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If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

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If a point is on the perpendicular bisector of a segment, the it is equidistant from the endpoints of the segment

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equidistant: if a point is the same distance from two objects

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equidistant: if a point is the same distance from two objects

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If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long

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mid segment of a triangle: a segment connecting the midpoints of two sides of the triangle

# data[].attributes.subject
mid segment of a triangle: a segment connecting the midpoints of two sides of the triangle