Geometry Chapter 3-4 Flashcards
If a point is equidistant from the sides of an angle
Then it is on the bisector of the angle
Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are congruent to the corresponding parts of another, then the triangles are congruent.
b=b’ , c=c’ , and angle A=Angle A’ then triangle ABC= Triangle A’B’C’
An equiangular triangle…
Is equilateral
if angle A=angle B=angle C, then AB=BC=CA
Corresponding angles are…
congruent
If the sides of two angles are respectively parallel to each other…
the angles are either congruent or supplementary
Transversal Line
a line that cuts across two or more parallel lines.
EF is a transversal of AB and CD
If a point is on the bisector of an angle
then it is equidistant from the sides of the angle
Two points each equidistant from the ends of a line segment determine
the perpendicular bisector of the line segment
if a pair of interior angles on the same side of a transversal are supplementary
the lines are parallel.
Corresponding Angles
two lines cut by a transversal are angles on the same side of the transversal and on the same side of the lines.
angle 1 and angle 2 are corresponding angles of AB and CD cut by transversal EF. Both angles are to the right of the transversal and both are below the line.
An equilateral triangle…
Is equiangular
if AB=BC=CA, then angle A=angle B=angle C
Parallel-Line Postulate
Through a given point not on a given line, one and only one line can be drawn parallel to a given line.
Alternate interior angles
two lines cut by a transversal that are nonadjacent angles between the two lines and on opposite sides of the transversal.
Angle 1 and angle 2 are alternate interior angles of AB and CD cut by EF.
If a Pair of corresponding angles are congruent
the two lines are parallel
two lines are parallel if each pair of interior angles on the same side of the transversal are…
supplementary
If two sides of a triangle are congruent…
the angles opposite these sides are congruent. (Base angles of an isosceles triangle are congruent)
If AB=BC then angle A=angle C
If two angles of a triangle are congruent
the sides opposite these angles are congruent
IF angle A=Angle C, then AB=BC
Each pair of alternate interior angles are congruent
If two lines are parallel
The perpendicular bisectors of the sides of a triangle meet…
in a point which is equidistant from the vertices of the triangle.
If two triangles are congruent…
then their corresponding parts are congruent
If lines are parallel, a line parallel to one of them is…
Parallel to the others also
If a pair of alternate interior angles are congruent
Then the two lines are parallel.
Perpendiculars to the same line
are parallel
Side-Side-Side (SSS)
If three sides of one triangle are congruent to three sides of another, then the triangles are congruent
If a=a’ , b=b’ , and c=c’ then triangle ABC= triangle A’B’C
Angle Side Angle (ASA)
If two angles and the included side of one triangle are congruent to the corresponding parts of another then the triangles are congruent.
If angle A=angle A’, angle C=angle C’, and b=b’ then triangle ABC=triangle A’B’C’
If a point is equidistant from the ends of a line segment
then it is on the perpendicular bisector of the line segment
if PA=PB then P is on CD, the perpendicular bisector of AB
Interior Angles
Formed by two lines cut by a transversal and the angles between the two lines, while exterior angles are those outside the lines.
the interior angles are 1,2,3,4 and the exterior angles are 5,6,7,8
If a point is on the perpendicular bisector of a line segment…
then it is equidistant from the ends of the line segment
If lines are parallel, a line perpendicular to one of them is…
perpendicular to the others as well.
The bisectors of the angles of a triangle meet
in a point which is equidistant from the sides of the triangle
