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geometry ch. 3
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Gravity
Terms in this set (36)
theorem 19
all radii of a circle are congruent
theorem 20
if two sides of a triangle are congruent, the angles opposite the side are congruent
theorem 21
if two angles of a triangle are congruent, the sides opposite the angles are congruent
2 Unnumbered theorems on p 149
if two sides of a triangle are not congruent, then the angles opposite them are not congruent and the larger angle is opposite the longer side
if two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle
SSS triangle congruency postulate
if there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent
SAS triangle congruency postulate
if there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent
ASA triangle congruency postulate
if there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent
AAS triangle congruency postulate
if two angles and one side of a triangle are congruent to the corresponding two angles and one side of a second triangle the triangle are congruent
Acute triangle
triangle in which all angles are acute
Altitude
line segment drawn from any vertex of the triangle to the opposite side, extended if necessary, and perpendicular to that side; forms right angle
Auxiliary line
additional lines that are drawn into the diagram
Base(isos. Triangle)
The segment formed by the two equal legs in an isosceles triangle.
Base angles
The angels formed by the two equal legs in a triangle.
Centroid
The point where the three medians of the triangle intersect.
Congruent polygons
all pairs of corresponding parts are congruent
Congruent triangles
all pairs of corresponding parts are congruent
Circle
the set of all points in plane that are equidistant from a given point
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Diameter
the distance across the circle, through it center
Equilateral triangle
triangle in which all sides are congruent
Equiangular triangle
triangle in which all angles are congruent
Hypotenuse
the side opposite the right angle
HL Postulate
if there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent
Included angle
the angle between two sides of a triangle
Included side
the side between two angles of a triangle
Isosceles triangle
triangle in which at least two sides are congruent
Leg
sides that form a right triangle
Median
segment whose endpoint are vertex of the triangle and the midpoint of the opposite side
Obtuse Triangle
triangle in which one of the angles is an obtuse angle
Orthocenter
the point where all three altitudes of the triangle intersect.
Radius
the distance from the center to a point on the circle
Reflexive Property
any segment or angle is congruent to itself
Right Triangle
triangle in which one of the angles is a right angle.
Scalene Triangle
triangle in which no two sides are congruent
Vertex angle (isos. Triangle)
the angle associated with a vertex of a polygon.
Six conclusions that can be drawn from a triangle congruency statement
sss
asa
sas
aas
hl
cpctc
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