4.1 And 4.2 Flashcards
Equilateral triangle
A triangle that has three congruent sides ( classifacation by sides)
Congruent triangles
If triangle Abc is congruent to triangle pqr then there is a correspondence between their angles and sides such that angles are congruent and corresponding sides are congruent.
Isosceles triangle
A triangle that has at least two congruent sides ( classifacation by sides)
Scalene triangle
A triangle that has no congruent sides ( classification by sides )
Acute triangle
A triangle that has 3 acute angles. If these angles are all congruent then the triangle is also equiangular. ( classification by angles )
Equiangular triangle
A triangle that has three congruent angles ( classification by angles)
Right triangle
A triangle that has exactly one right angle ( classification by angles )
Obtuse triangle
A triangle that has exactly one obtuse angle ( classifacation by angles)
Vertex
In triangle abc each of the points a b and c are vertces of the triangle
Opposite side
The Side opposite if a given angle
Adjacent side
Two sides that share a common vertex are adjacent sides
Right triangle legs
The sides adjacent to the right triangle are the right triangle legs
Right triangle hypotenuse
The side opposite of the right angle is the hypotenuse of the the triangle
Isosceles triangle legs
An isosceles triangle can have three congruent sides. If it has only two, then the two congruent sides are the legs of the triangle
Isosceles triangle based
The third side is the base of the triangle
Theorem 4.1: properties of congruent triangles-
- Every triangle is congruent to itself
- If triangle abc is congruent to triangle pqr and triangle pqr is congruent to triangle tuv then triangle abc is congruent to triangle tuv
- If triangle abc is congruent to triangle pqr then triangle pqr is congruent to triangle abc
Interior able
Three angles f a triangle
Exterior angle
An angle that is adjacent to an interior angle ( must form a linear pair)
Theorem 4.2 : triangle sum theorem
The sum of the measures of the interior angles of the triangle is 180 degrees
Theorem 4.3: third angles theorem
If two angles of one triangle are congruent to two angles of a second triangle then the Thor angles are also congruent
Theorem 4.4
The acute angles of a right triangle are complementary
Thereom 4.5 exterior angles theorem
The measure of an exterior angle of a triangle is equal to the sum of the measure of the two remote ( non adjacent ) interior angles
Theorem 4.6: exterior Angles inequality theorem
The measure of an exterior angle of a triangle is greater than the measure of either of the two remote ( non adjacent ) interior angles
Auxiliary line
Line added to a geometric figure
Name the four ways to prove triangles congruent
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