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Geometry Chapter 4
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Terms in this set (30)
triangle angle sum theorem
the sum of the measures of a triangle is 180
exterior angle theorem
the measure of an exterior angle of a triangle is the sum of the measures of the two remote interior angles
remote interior angles
two angles not adjacent to the exterior angle
corollary
a theorem with a proof that follows as a direct result
triangle angle sum corollary
the acute angles of a right triangle are complementary
acute triangle
3 acute angles
equiangular triangle
all angles are congruent
obtuse triangle
1 obtuse angle
right triangle
1 right angle
equilateral triangle
all sides are congruent
isosceles triangle
exactly 2 congruent sides
scalene triangle
no congruent sides
CPCTC
corresponding parts of congruent triangles are congruent
third angles theorem
If two angles of one triangle are congruent, the third angles are congruent
reflexive property of congruence
congruent to itself
symmetric property of congruence
can be written in either order
transitive property of congruence
if a is congruent to b and b is congruent to c then a is congruent to c
angle bisector
splits an angle into 2 congruent parts
midpoint
splits a segment into 2 congruent parts
SSS
All three sides are congruent in a triangle
SAS
two sides and their included angle are congruent in another triangle
ASA
two angles and their included side are congruent in another triangle
AAS
two angles and a non-included angle are congruent in another triangle
HL
the hypotenuse and leg of a right triangle are congruent to another right triangle
isosceles triangle theorem
if two sides of a triangle are congruent then the angles opposite those sides are congruent
converse of the isosceles triangle theorem
if two angles of a triangle are congruent then the sides opposite those angles are congruent
vertex angle
angle with the sides that are legs of an isosceles triangle
legs of an isosceles triangle
two congruent sides in a triangle
base angles
two angles formed by the base and the congruent sides of a triangle
equilateral triangle corollary
a triangle is equilateral if an only if it is equiangular (each angle measures 60 degrees)
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