Geometry Unit 4

• One-to-One Correspondence 


  The situation when each member if a set, such as angles of a triangle, can be paired with and only one member of another set.
• Corresponding Angles


  Angles paired with one another in a one-to-one correspondence.
• Corresponding Sides 


  Sides paired with one another in a one-to-one correspondence.
• Congruent Triangles


  If a one-to-one correspondence between the parts of the two triangles is such that the corresponding parts are equal, then the triangles are congruent.
• Included Angle 


  The angle formed by the two sides of a triangle.
• Included Side


  The side of a triangle that is formed by the common side of two angles.
• S.S.S.


  Side Side Side postulate
• Postulate 12 


  If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle then the triangles are congruent. (SAS)
• Postulate 11


  If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. (SSS)
• SAS


  Side Angle Side postulate
• Postulate 13 


  If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. (ASA)
• ASA


  Angle Side Angle postulate
• Theorem 4-1 


  If two angles and a not included side of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent. (AAS)
• AAS


  Angle Angle Side theorem
• Theorem 4-2


  If two legs of one right triangle are equal to two legs of another right angle triangle, then the two right triangles are congruent. (LL)
• LL


  Leg Leg theorem
• Postulate 14 


  If the hypotenuse and a leg of one triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent. (HL)
• HL


  Hypotenuse Leg postulate
• Theorem 4-3


  If the hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent. (HA)
• HA


  Hypotenuse Angle theorem
• Theorem 4-4


  If a leg and an acute angle of one right triangle are equal to the corresponding parts of another right triangle, then the triangles are congruent. (LA)
• LA 


  Leg Angle theorem
• Correspondence


  A relationship between the parts of two triangles, where each vertex and side of one triangle corresponds to a unique vertex and side of the other triangle.
• Congruent


  Two figures that have the same size and shape, so that if you move one figure on top of the other, they match up perfectly.
• Congruent triangles


  Two triangles that are congruent, meaning that there is a correspondence between their parts such that the corresponding parts are equal in length and measure.