CONGRUENT

TRIANGLE

S

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

&AB BC

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.

Engineering ApplicationThe 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 MProve: JKL JML JL bisects KLM K M Given

JL JL ReflexiveKLJ 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

BC CB Reflexive ABC & DCB are right angles Given

ABC & DCB are rt. s Def. right ABC DCB HL.

WAYS TO PROVE TRIANGLES

SSS SAS

AASASA

HL