Converse of Corresponding Angles Postulate
If 2 lines r intersected by a transversal, & corresponding angles are congruent, then the lines are parallel.
Converse of Cointerior Angles Theorem
If 2 lines r cut by a transv & cointerior angles r supp, then the lines r parallel
Converse of Alt Interior Angles Theorem
If 2 lines r cut by a transv & alt interior angles r congruent, then the lines r parallel
Perpendicular & Parallel Th
If 2 lines r perp 2 the same transversal, then they r parallel.
Perp & Transversal Th
If a transv is perp to one of two parallel lines, then it is also perp to the other line.
quadrilateral with only 1 pair of parallel sides
Triangle Sum Th
the sum of the measures of the angles of a triangle is 180
Quadrilateral Sum Th
The sum of the measures of the angles of a quadrilateral is 360.
Converse of Quadrilateral Th
If both pairs of opp angles of a quadrilateral r equal, then the quadrilateral is a parallelogram.
Exterior Angle Th
An exterior angle of a triangle is equal in measure to the sum of its 2 remote interior angles.
definition of similar
2 triangles are similar iff their vertices can be matched up so that the corresponding angles are equal & corresponding sides are in proportion.
definition of congruent
2 triangles r congruent iff their vertices can be matched up so that the corresponding parts (angles & sides) of the triangles r equal in measure.
Triangle Similarity Postulate (AA Post.)
If 2 angles of a triangle r equal to 2 angles of another triangle, then the 2 triangles are similar.
How to find any angle of a triangle?
A = 1/2ab sin C
SOH CAH TOA
Overlapping Similar Triangles
If a line is drawn from a point on one side of a triangle parallel to another side, then it forms a triangle similar to the original side.
If 2 angles & the included side of 1 triangle are equal to the corresponding angles and side of another triangle, then the triangles are congruent.
If 2 angles and a non-included side of 1 triangle r equal to corresponding angles and side of another triangle, then the triangles are equal.
ASS IZ NOT GOOD
If 2 sides & the included angle of 2 triangle r equal to the corresponding sides & angle of another triangle, then the triangles r congruent.
a ray that begins in the vertex of an angle & divides the angle into 2 equal parts
a ray, line, or segment that divides a segment into two equal parts
a line, ray, / segment that bisects the segment & is perpendicular to it
2 right triangles are equal if the hypotenuse & leg of 1 triangle are equal to the hypotenuse & leg of the other triangle
a triangle w/ 2 sides = in measure
a triangle in which all the sides are equal in measure
a triangle in which all the angles are equal in measure
Isosceles Triangle Theorem
If 2 sides of a triangle r = in measure, then the angles opposite those sides are = in measure
Converse of Isosceles Triangle Th
If 2 angles of a triangle r equal in measure, then the sides opposite those angles r = in measure
Equilateral Triangle Th
If a triangle is equilateral, then it's also equiangular