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20 terms

Geometry Chapter 4, 5 Congruent Triangles

Chapter 4 (McDougall Littell) Geometry terms, theorems, postulates, etc.
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Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
congruent polygons
are congruent only if all corresponding parts are congruent
corresponding part
the part of one shape has to be congruent to that same corner on the other shape
SSS
If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent
SAS
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
ASA
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
AAS
If two angles and a NON-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
HL
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. *Only for use of right triangles
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then the point is an equal distance from the endpoints of the segment
legs of isosceles triangle
are opposite base
base of isosceles triangle
opposite two legs
base angle of isosceles triangle
congruent angles on the base
vertex angle
point at which the two legs meet (opposite base)
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite the sides are congruent
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angle are congruent
median of a triangle
a segment from a vertex to the midpoint of the opposite side
altitude of a triangle
perpendicular segment from a vertex to the line that contains the opposite side
SSA
Side-side-angle does NOT prove triangle congruence; exception is with a right triangle (see HL)
CPCTC
Corresponding parts of congruent triangles are congruent; once two triangles have been proven congruent (by using SSS, SAS, ASA, AAS, or HL), then we can conclude its parts are congruent through CPCTC
AAA
Angle-angle-angle does NOT prove triangle congruence (however, triangles will be similar; only need AA to prove similarity)