Chapter 5: Triangles Flashcards
A polygon is
a geometric figure whose sides are line segments
A triangle is
a polygon that has three sides
A scalene triangle has
no congruent (equal) sides
An isosceles triangle has
at least two congruent (equal) sides
An equilateral triangle has
all three congruent (equal) sides
An acute triangle has
all three angles with measure of less than 90
A right triangle has
one angle with a measure of 90
obtuse triangle
has one angle with a measure of greater than 90
Theorem 16: If two lines are parallel to a third line,
then the lines are parallel to each other
Postulate 8: Through a given point not on a line,
exactly one line may be drawn parallel to the line
Theorem 17: The sum of the measures of the angles of a triangle is
180
Corollary 17.1: The acute angles of a right triangle are
complementary
Corollary 17.2: The measure of each angle of an equiangular triangle is
60
Corollary 17.3: If two angles of a triangle are congruent to two angles of another triangle,
then the remaining pair of angles is congruent
Exterior Angle of a Polygon
an angle that forms a linear pair with one of the interior angles of the polygon
An equiangular triangle has
all three angles with equal measures
Theorem 18: Exterior Angle of a Triangle Theorem: The measure of an exterior angle of a triangle is equal to
the sum of the measures of the two remote interior angles
Definition of Congruent Triangles:
If the vertices of two triangles can be paired in a correspondence so that all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent, then the triangles are congruent.
Postulate 9: Side-Angle-Side Postulate: If the vertices of two triangles can be paired so that two sides and the included angle of one triangle are congruent to the corresponding parts of the second triangle,
then the two triangles are congruent
Postulate 10: Angle-Side-Angle Postulate: If the vertices of two triangles can be paired so that the two angles and the included side of one triangle are congruent to the corresponding parts of the second triangle,
then the two triangles are congruent
Theorem 19: Angle-Angle-Side Theorem: If the vertices of two triangles can be paired to that two angles and the side opposite one of the in one triangle are congruent to the corresponding parts of the second triangle,
then the two triangles are congruent
Postulate 11: Hypotenuse-Leg Postulate: If the vertices of two right triangles can be paired so that the hypotenuse and leg of one of them are congruent to the corresponding parts of the second triangle, then
the two triangles are congruent
Postulate 12: Side-Side-Side Postulate: If the vertices of two triangles can be paired so that three sides of one triangle are congruent to the corresponding sides of the second triangle, then
the two triangles are congruent
