CONGRUENT TRIANGLES
How To Find Congruent Sides ? ? Remember to look for the following: Adjacent triangles share a COMMON SIDE, so you can apply the REFLEXIVE Property to get a pair of congruent sides. Look for segment bisectors.. They lead to midpoints…. Which lead to congruent segments.
Use SSS to explain why ∆ABC ∆CDA. AB CD and BC DA Given AC CA Reflexive ∆ABC ∆CDA SSS
An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between
How To Find Congruent ANGLES ? ? Remember to look for the following: Look for VERTICAL ANGLES. Look for lines. They form adjacent angles. Look for // LINES CUT BY A TRANSVERSAL. They lead to angles. Look for < bisectors. They lead to angles.
The letters SAS are written in that order because the congruent angles must be INCLUDED between pairs of congruent corresponding sides.
XZY VZW VERTICAL <‘s are Engineering Application The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ ∆VWZ. XZ VZ YZ WZ Given XZY VZW VERTICAL <‘s are ∆XYZ ∆VWZ SAS .
An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.
When using ASA , the side must be INCLUDED between the angles known to be congruent.
Determine if you can use ASA to prove NKL LMN. Explain. KL and NM are //. KLN MNL, because // lines imply alt int >s. NL LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied.
When using AAS , the sides must be NONINCLUDED and opposite corresponding angles.
Use AAS to prove the triangles Given: JL bisects KLM K M Prove: JKL JML JL bisects KLM K M Given JL JL Reflexive KLJ MLJ Def. < bis. JKL JML AAS
When using HL , you must FIRST state that there is a RIGHT TRIANGLE!
Determine if you can use the HL Congruence Theorem to prove ABC DCB. AC DB Given ABC & DCB are right angles Given BC CB Reflexive ABC & DCB are rt. s Def. right ABC DCB HL.
Ways to prove triangles SSS SAS HL ASA AAS