Unit 4 Flashcards
The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of a second triangle, then the third angle of the first triangle will also be congruent to the _____ angle of the second triangle.
Third
Which theorem or corollary could be used to prove the conjecture?
Conjecture: m(1= m(2+ (M3
Exterior angle theorem
A corollary of the Triangle Sum Theorem states that a triangle can contain no more than one _____ angle or obtuse angle.
Right
A segment that joins any two nonadjacent vertices of a polygon is a(n) _____.
Diagonal of a polygon
A statement whose proof can be deduced directly from a previous theorem is a(n) _____.
Corollary
A(n) _____ is any side of a polygon that shares a side with only one angle of a pair of angles.
nonincluded side
A polygon that is equiangular but not equilateral, or equilateral but not equiangular, or neither equiangular nor equilateral is a(n) _____.
irregular polygon
_____ are polygons in which their corresponding angles and sides are congruent.
Congruent Polygons
A polygon in which any of its diagonals contain points in the exterior of the polygon is a(n) _____.
Concave polygon
Two angles are congruent, therefore the sides opposite those angles are congruent.
Converse to the Isosceles Triangle Theorem
_____ sides or angles are in the same relative position on two different polygons that have the same number of sides and angles.
Corresponding
A polygon that is both equiangular and equilateral is a(n) _____.
regular polygon
Whats the formula from the interior polygon
(N-2)180
All three angles are congruent, therefore all three angles are congruent.
Corollary to the Converse of the Isosceles Triangle Theorem
A(n) _____ is an angle formed by the intersection of two adjacent sides of a polygon.
Included angle
An interior angle of a polygon that is not adjacent to a particular exterior angle is a(n) _____.
Remote interior angle
A segment that joins any two nonadjacent vertices of a polygon is a(n) _____.
Diagonal of a polygon
A polygon in which none of its diagonals contain points in the exterior of the polygon is a(n) _____.
convex polygon
A triangle with at least two congruent sides is a(n) _____.
Isosceles triangle
Two sides are congruent, therefore, the angles opposite those sides are congruent.
Isosceles Triangle Theorem
All three sides are congruent, therefore all three angles are congruent.
Corollary to the Isosceles Triangle Theorem
The triangles are congruent, therefore their corresponding parts are congruent.
CPCTC
Any side of a polygon that shares a side with only one angle of a pair of angles is a(n) _____ side.
Nonincluded
The _____ of a right triangle is the side opposite the right angle.
Hypotenuse
A special kind of triangle with no congruent sides.
scalene
The Polygon Exterior Angle sum Theorem states that the sum of the measures of the exterior angles, one angle at each vertex, of a convex polygon is _____.
360
