Goal 1

1. Goal 1 Identifying Congruent Figures Two geometric figures are congruent if they have exactly the same size and shape. Each of the red figures is congruent to the other red figures. None of the blue figures is congruent to another blue figure.

2. Goal 1 Identifying Congruent Figures For the triangles below, you can write , which reads “triangle ABCis congruent to triangle PQR.” The notation shows the congruence and the correspondence. AB  PQ PQR ABC BCA QRP BC  QR CA  RP There is more than one way to write a congruence statement, but it is important to list the corresponding angles in the same order. For example, you can also write  . When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent. Corresponding Angles Corresponding Sides  A P  B Q  C R

3. Example Naming Congruent Parts The diagram indicates that  . The congruent angles and sides are as follows. DEF RST   , , FD TR EF ST DE RS The two triangles shown below are congruent. Write a congruence statement. Identify all pairs of congruent corresponding parts. SOLUTION Angles:  DR, ES, FT Sides:

4. Example Using Properties of Congruent Figures You know that  . LM GH In the diagram, NPLM EFGH. Find the value of x. SOLUTION So, LM= GH. 8 = 2x– 3 11 = 2x 5.5 = x

5. Example Using Properties of Congruent Figures You know that  . LM GH In the diagram, NPLM EFGH. Find the value of x. Find the value of y. SOLUTION SOLUTION You know that NE. So, m N= m E. So, LM= GH. 72˚ = (7y+ 9)˚ 8 = 2x– 3 63 = 7y 11 = 2x 9 = y 5.5 = x

6. Example Proving Two Triangles are Congruent Prove that  . AEB DEC A B E || , AB DC D C E is the midpoint of BC and AD. GIVEN  . PROVE AEB DEC Plan for Proof Use the fact that AEB and  DEC are vertical angles to show that those angles are congruent. Use the fact that BC intersects parallel segments AB and DC to identify other pairs of angles that are congruent.  , AB DC

7. Example Proving Two Triangles are Congruent Prove that  . AEB DEC  EAB   EDC, A B  ABE   DCE E D C  || , AB DC AB DC E is the midpoint of AD, E is the midpoint of BC ,  AE BE CE DE  DEC AEB SOLUTION Given Alternate Interior Angles Theorem Vertical Angles Theorem  AEB   DEC Given Definition of midpoint Definition of congruent triangles

8. CPCTC • What does this mean? • Corresponding parts of   are . • Why do we need this? • proofsssss •  jk- these are easy! • The 2 triangles are  so complete each statement. • PXY  _____ • P  ____ because (b/c) ____ • XP  ____ b/c __________ • 1  ____ b/c __________ • Then YX bisects PYT b/c __________________________. P 1 Y 2 X T

9. Practice, Practice, Practice • Suppose TIM BER. Complete each statement. • IM  _____ • _____   R • MTI   _______ • If  ABC   XYZ, m B = 80, and m C= 50, name 4 congruent angles. Classify each triangle.

10. Always, Sometimes, Never • An acute triangle is _________ congruent to an obtuse triangle. • A polygon is __________ congruent to itself. • A right triangle is ___________ congruent to another right triangle. • If  ABC   XYZ, B is _______ congruent to Y. • If ABC  XYZ, AB is _________ congruent to YZ.