Geometry Test #4 Flashcards
Sum of the Interior Angles of a Triangle and its Corollaries
Recall: The sum of the measures of the interior angles of a triangle is 180.
Corollaries:
1. If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent to each other.
2. The measure of each angle of an equilateral triangle is 60.
3. In a triangle, there can be at most one right angle.
4. The acute angles of a right triangle are complementary.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 remote interior angles.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of any of its remote interior angles.
Triangle Inequality Theorem
a. The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side.
b. The positive difference of the lengths of any 2 sides of a triangle is less than the length of the third side.
Polygon
A polygon is a closed 2D figure formed by straight line segments. Each segment must intersect with exactly 2 other segments at each endpoint. A polygon should have at least 3 sides.
Regular Polygon
Equiangular and Equilateral
Convex Polygon
All interior angles are less than 180.
Concave Polygon
1 or more interior angles is more than 180.
Diagonal of a Polygon
A segment joining 2 nonconsecutive vertices.
Sum of all interior angles
180(n-2)
Measure of one interior angle
180-(360/n)
Measure of one exterior angle
360/n
Sum of all exterior angles
360
If two lines are cut by a transversal,
then corresponding angles are congruent.
If two lines are cut by a transversal and corresponding angles are congruent,
then the lines are parallel.
Vertical Angles are Congruent
Vertical Angles are Congruent
If two lines are perpendicular,
then they form congruent adjacent angles.
If two lines form congruent adjacent angles,
then the lines are perpendicular.
If the exterior sides of two adjacent acute angles are perpendicular,
then the two angles are congruent
If two angles are supplements of congruent angles (or of the same angle),
then the two angles are congruent
If two angles are complements of congruent angles (or of the same angle),
then the two angles are congruent
3.1
If two parallel planes are cut by a third plane,
then the lines of intersection are parallel.
3.2
If two parallel lines are cut by a transversal,
then alternate interior angles are congruent
3.3
If two parallel lines are cut by a transversal,
then s-s int. angles are supp..
3.4
If a transversal is perpendicular to one of two parallel lines,
then it is perpendicular to the other one also.
3.5
If two lines are cut by a transversal and alternate interior angles are congruent,
then the lines are parallel.
3.6
If two lines are cut by a transversal and s-s int angles are supp,
then the lines are parallel.
In a plane two lines perpendicular to the same line are
parallel
3.8
Through a point outside a line,
there is exactly one line parallel to each other.