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123 Cards in this Set
- Front
- Back
Supplement theorem
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If two angles form a linear pair then they are supplementary angles
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complement theorem
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if the noncommon sides of two adjacent angles form a right angle then the angles are complementary angles.
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congruence of angles
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are reflexive, symetric, and transitive
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Theorem angles suppl to the...
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angles suppl to same angle or congruent angles are congruent
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theorem
angles compl |
angles compl to same angle or congru. angles are congru
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vert angle theorem
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if two angles are vert angles then they ar congru
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perpendicular lines intersect to
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to form 4 right angles
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all right angles are
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congruent
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Perpendicular lines form..
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congruent adj angles.
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if two lines are congruent and suppl then
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each angle is a rght angle
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if 2 congru angles form a linear pair then
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they are right angles
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CA means
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if 2 lines are //, cut by a transversal, then each pr of corre angles is con.
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AIA
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If 2 // lines cut by a trans then each pr of aia is con
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CIA
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If two // lines cut by transve then ea pr of consec int angl is suppl
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AEA
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If 2 // lines cut by transve then each pr of AEA is congruent
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Perpen transversal TH
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in a plane, if a line is perpen to one then perpen to other
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2 nonvertical lines have the same slope
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if and only if they are //
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2 nonvert lines are perpen
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if and only if the product of their slopes are -1
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if 2 lines in a plane are cut by a trans
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so that the corres angles are congru then the lines are //
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// post
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if there is a line and a point not on al ine then there exsist one line that is exactly one though the pnt that is // to given line
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if alt ext angles are congru then..
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lines are //
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if cons int angles are suppl then
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the lines are //
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if alt angles are congru then...
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the lines are //
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if 2 lines are perpen to the samelines then
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they are //
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in a plane if 2 lines are each equidistant from the thrid
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then two lines are // to ea other
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Angle sum TH
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The sum of a whole tiangle is 180
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third angle TH
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If 2 angles of one triangle are congruent to 2 angles of a second tri then the 3rd angles of the tri are congru
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EXT angle TH
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The measure of an ext angle of a tri is equall to the sum of the measures of the two remot int angles
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the acute angles of a rght tri are
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are comple
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There can only be 1 blank and 1 balnk in a tri at most
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right and obtuse
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congruence of tri is
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reflex symm, and transitive
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SSS
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If the side of one tri is congru to the sides of the second tri then the tri are congru
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SAS
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if 2 sides and the inclu side of one triangle are congru to 2 sides and the inclu of another tri the tri are con
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ASA
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If 2 angles and the inclu side of one tri are con to 2 and the sides and the inclu angle of another tri then tris are congru
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AAS
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angle angle side
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LL
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if the legs of a right tri are con then the tri are congru
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HA
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if the hypotenuse and acute of one rght tri , and the hypo is con to the acuute then the tris are congru
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LA
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If a leg and a acute angle are con on a rght tri then tris are congru
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HL
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If the Hypo and leg are con in a rght tri then tris are con
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Con isos TH if 2 angles of a tri are congu
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then the sides opp angles are congru
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I tri is =lateral if
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it it is = angular
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ea of an equilangular tri measurs
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60
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ANy point on the perpen bisect of a seg is =distant from the
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endpoint of a segment
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any point on a =distant from the endpoints of a seg lies on the perpen
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bisector of the seg
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circum center TH
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The circumcenter of a tri is equal dist from the vercies of the tri
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ANy point on the bisect is equal dist from the sides of an angle lies
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on the angle bisect
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incenter TH
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The incenter of a tri is = dist from ea side of the tri
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CEntroid Th
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The centroid of a tri is located 2/3 of teh dist from a vert to the midpt of te opp the vertex on a median
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Ext Angle In=ity TH
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If an angle is an EXT angle of a tri then its measure is greater than the measure of either of its corr remote int angles
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if one angle of a tri has a greater measure than another angles
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then the side opp the greate angle is longer than the side opp the lesser angle
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The perpen seg from a point to a line is
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shortest seg from point to the line
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The perpern seg from a pnt to a place is
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the shortest seg from point to the plane
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tri in= th
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the sum of any two sides of a tri id greater thsnthe 3rd side
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acute angle
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An angle of less than 90°.
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acute tri
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triangle whose interior angles are all acute
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adj andgles
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Either of two angles having a common side and a common vertex
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AEA
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Angles 1, 2, 3, and 4 are all exterior angles. Angles 1 and 4 are alternate exterior angles. Angles 2 and 3 are also alternate exterior angles. Line t (in red) is called a transversal, a line crossing two or more lines.
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AIA
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Angles 1 and 4 are alternate interior angles. Angles 2 and 3 are also alternate interior angles. Line t (in red) is called a transversal, a line crossing two or more lines. When the transversal cuts through 2 parallel lines, the alternate interior angles formed have a special relationship
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altitude
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The perpendicular distance between a vertex of a triangle and the side opposite that vertex. Sometimes called the height of a triangle. Also, sometimes the line segment itself is referred to as the altitude
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angle
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Region between two rays
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angle bisector
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A segment or ray that shares a common endpoint with an angle and divides the angle into two equal parts.
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Biconditional
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a conjunction of a conditional state and its conve
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centroid
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The point of intersection of the medians of a triangle.
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circumcenter
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point of intersection of the perpendicular bisectors of the sides of a given triangle
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collinear
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Points are collinear if they lie on the same straight line.
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compl angles
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Complementary angles are two angles whose sum is 90 degrees.
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conclusion
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the statement that follows the word then
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concurrent lines
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3 or more lines that inter sect at a common point
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condition stat
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a if then state
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congruent
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having the same measure
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congruent tri
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Triangles that have the same size and shape.
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conjecture
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an educated guess based on known info
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CIA
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the 2 middle top bottom #
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contrapt
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formed statement from the converse of a state
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converese
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The statement formed by hypo and conlu of the converse of a conditional state
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convex poly
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a polygon where no line contains both sides of the poly gon
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coplaner
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Set of points, lines, rays, line segments, etc., that lie in the same plane
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corresponding angles
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Angles that have the same relative positions in geometric figures.
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counter example
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to show that a state isnt always true
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condition stat
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a if then state
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hypothesis
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follows the word if the condition stat
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congruent
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having the same measure
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if-then statement
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a compound statement it goes if A then B
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congruent tri
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Triangles that have the same size and shape.
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disjunction
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a compound statement frmed by joining 2 or more statements
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conjecture
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an educated guess based on known info
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incenter
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The center of a circle inscribed in a given triangle.
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CIA
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the 2 middle top bottom #
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contrapt
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formed statement from the converse of a state
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converese
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The statement formed by hypo and conlu of the converse of a conditional state
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convex poly
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a polygon where no line contains both sides of the poly gon
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coplaner
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Set of points, lines, rays, line segments, etc., that lie in the same plane
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corresponding angles
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Angles that have the same relative positions in geometric figures.
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counter example
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to show that a state isnt always true
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hypothesis
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follows the word if the condition stat
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if-then statement
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a compound statement it goes if A then B
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disjunction
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a compound statement frmed by joining 2 or more statements
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incenter
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The center of a circle inscribed in a given triangle.
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condition stat
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a if then state
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congruent
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having the same measure
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congruent tri
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Triangles that have the same size and shape.
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conjecture
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an educated guess based on known info
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CIA
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the 2 middle top bottom #
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contrapt
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formed statement from the converse of a state
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converese
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The statement formed by hypo and conlu of the converse of a conditional state
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convex poly
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a polygon where no line contains both sides of the poly gon
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coplaner
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Set of points, lines, rays, line segments, etc., that lie in the same plane
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corresponding angles
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Angles that have the same relative positions in geometric figures.
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counter example
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to show that a state isnt always true
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hypothesis
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follows the word if the condition stat
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if-then statement
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a compound statement it goes if A then B
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disjunction
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a compound statement frmed by joining 2 or more statements
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incenter
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The center of a circle inscribed in a given triangle.
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included angle
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an angle formed by 2 sides
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included side
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the side of the tri the is part of the 2 angles
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indirect proof
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when you use the assume
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inductive reasoning
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arrived by deductive reasoning
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inverse
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negating both the hypothesis and conclusion
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isoscelese tri
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A triangle with at least two sides having equal lengths.
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law of detachment
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if p then q is true p is true, then so is q
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line
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One of the basic undefined terms of geometry. A line has no thickness but its length goes on forever in two directions., at least 2 pnts
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line seg
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The part of a line between two points on the line. Sometimes referred to as a segment.
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linear pair
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Two adjacent angles that form a straight line
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