If B is the If two angles are

Transcription

1 If If B is between A and C, then 1 2 If P is in the interior of RST, then If B is the If two angles are midpoint of AC, vertical, then then 3 4 If angles are adjacent, then If angles are a linear pair, then 5 6 If angles are If angles are supplementary, complementary, then then 7 8

2 Angle Add. Post. m RSP m PST m RST Seg. Add. Post. AB BC AC 2 1 they are formed by 2 pairs of opposite rays. 4 3 AB BC 2 adjacent angles whose noncommon sides form opposite rays. 6 5 Their sum is 90 degrees. They share a common vertex and side. Their sum is 180 degrees. 8 7

3 If lines are perpendicular, then 9 10 If there is a line, then If two points, then If two lines intersect, then If two planes intersect, then If there is a plane, then If there are at least 3 noncollinear points, then If two points lie in the plane, then

4 There is exactly one line. They form right angles Their There is at least intersection is a 2 points. point The plane contains at least 3 noncollinear points A line containing those points lies in the plane Their intersection is a line. There is exactly one plane.

5 If a ray bisects an angle, then Conditional Statement Converse Inverse Contrapositive If a segment bisector, then If polygons is equilateral, then If polygon is equiangular, then

6 If hypothesis, then conclusion Negation of the original conditional The ray forms 2 pairs of congruent angles. Switching the hypothesis and conclusion of the original conditional It finds the midpoint Negation of the converse All angles are congruent All sides are congruent

7 If polygon is regular, then Undefined terms of Geometry What is the name for 1& 2? What is the name for 1& 2? What is the name for 1& 2? What is the name for 1& 2? If two parallel lines are cut by a transversal, then consecutive interior angles are. If two parallel lines are cut by a transversal, then corresponding angles are

8 Point, Line, and Plane It is convex and all sides and angles are congruent Consecutive interior angles Corresponding angles Alternate interior angles Alternate exterior angles congruent supplementary 32 31

9 If two parallel lines are cut by a transversal, then alternate interior angles are If two parallel lines are cut by a transversal, then alternate exterior angles are. If a transversal, then If skew lines, then Name the Name the property property QW=QW MN=HJ, HJ=MN Name the property If AB=DE and DE=RT, then AB=RT Name the property If DE=GH+5 and GH=x, then DE=x

10 congruent congruent The lines do not intersect and are noncoplanar A line that intersects two other lines Symmetric Property Reflexive Property Substitution Property Transitive Property 40 39

11 Linear Pair Postulate Right Angle Vertical Angles congruence theorem Right Angles congruence theorem Corresponding angles postulate Alternate Interior angles theorem Consecutive interior angles theorem Alternate exterior angles theorem

12 Vertical Angles are congruent If two angles form a linear pair, then they are supplementary All right angles are congruent An angle that measures 90 degrees If parallel lines are cut by transversal, then consecutive interior angles are supplementary If parallel lines are cut by transversal, then alternate exterior angles are congruent If parallel lines are cut by transversal, then corresponding angles are congruent. If parallel lines are cut by transversal, then alternate interior angles are congruent.

13 Converse Corresponding angles postulate Converse alternate interior angles theorem Converse Consecutive interior angles theorem Converse alternate exterior angles theorem Triangle Sum Exterior Angle Corollary to Triangle Sum Third Angle

14 If consecutive interior angles are supplementary, then the lines are parallel If alternate exterior angles are congruent, then the lines are parallel If corresponding angles are congruent, then the lines are parallel. If alternate interior angles are congruent, then the lines are parallel. The measure of the exterior angle is equal to the sum of the two nonadjacent interior angles If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent The sum of the interior angles of a triangle is 180. The acute angles of a right triangle are complementary

15 SSS Congruence Postulate SAS Congruence Postulate ASA Congruence Postulate AAS Congruence Hypotenuse Leg Congruence Converse of the Base Angles Base Angles CPCTC

16 If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent If two sides and an included side of one triangle are congruent to an included angle and two sides of an another triangle, then the triangles are congruent. If two angles and the included side of one triangle are congruent to two angles and the include side of another triangle, then the triangles are congruent If two angles and a nonincluded side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent If two angles of a triangle are congruent, then the sides opposite them are congruent If two side of a triangle are congruent, then the angles opposite them are congruent. Corresponding Parts of Congruent Triangles are Congruent

17 Congruent Supplement Equilateral Triangle Congruent Complement Isosceles Triangle Scalene Triangle Midsegment of a Triangle Perpendicular Bisector Median of a triangle 71 72

18 If two angles are complementary to the same angle (or to congruent angles), then the two angles are congruent If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent. Triangle with 2 congruent sides Triangle with 3 congruent sides A segment that connects the midpoints of two sides of the triangle A segment from one vertex of the triangle to the midpoint of the opposite side Triangle with no congruent sides A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

19 Altitude of a Triangle Angle Bisector of a Triangle Circumcenter Incenter Centroid Orthocenter Perpendicular Bisector Converse of Perpendicular Bisector

20 A segment from one vertex of a triangle to the side opposite and divides the angle into two congruent angles The point of concurrency of the three angle bisectors of the triangle. The point is equidistant from the sides of the triangle The perpendicular segment from one vertex of the triangle to the opposite side or to the line contains the opposite side. The point of concurrency of the three perpendicular bisectors of the triangle. It is equidistant from the vertices. The point of concurrency of the three altitudes of the triangle If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment The point of concurrency of the three medians of the triangle. The point is two thirds the distance from each vertex to the midpoint of the opposite side. If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

21 Angle Bisector Converse of the Angle Bisector If one side of a triangle is longer than another side, then If one angle of a triangle is larger than another angle, then Hinge If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then Converse of Hinge If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then Triangle If two polygons Inequality are similar, then 87 88

22 If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle The side opposite the larger angle is longer than the side opposite the smaller angle If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. The angle opposite the longer side is larger than the angle opposite the shorter side. The included angle of the first is larger than the included angle of the second The ratio of their perimeters is equal to the ratios of their corresponding side lengths The third side of the first is longer than the third side of the second. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

23 Side-Side-Side Side-Angle-Side Similarity Similarity Angle-Angle Similarity Postulate Triangle Proportionality Converse of the Triangle Proportionality If three parallel lines intersect two transversals, then If a ray bisects an angle of a triangle, then Proportion

24 If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar If the corresponding side lengths of two triangles are proportional, then the triangles are similar. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. they divide the transversals proportionally extreme mean mean extreme An equation of two equal ratios If a line divides two sides of a triangle proportionally, then it is parallel to the third side. It divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

25

26