Download 4.2 Apply Congruence and Triangles

4.2 Apply Congruence and Triangles Goal  Identify congruent figures.
Congruent figures: In two congruent figures, all the parts (sides and angles) of one figure are
_____________________ to the corresponding parts (sides and angles) of the other figure.
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding
parts.
.
something  something
Corresponding sides :
Corresponding angles:
AB  _______
A  ________
To help you identify
corresponding parts,
turn  FGH
CB  ________
B  ________
CA  ________
C  ________
So, ABC  _________________ (YOU MUST GET THESE LETTERS IN THE RIGHT ORDER!)
In the diagram, QRST  WXYZ.
A. Find the value of x.
B. Find the value of y.
Use the diagram shown in which FGHJ  STUV.
1.
Identify all pairs of congruent corresponding parts.
Corresponding angles: F ______, G  ______, H  ______, J  _______
Corresponding sides: HJ
 ______
JF _______ FG _______
GH  _______
2. Find the value of x and find mG.
THEOREM: THIRD ANGLES THEOREM
If two angles of one triangle are ________________to two angles of another triangle, then the third
angles are also ________________________.
Use the Third Angles Theorem
Find mV.
Example - In the diagram, EFG  OPQ. Complete the statement.
1. EF  ____
2. P  ____
F
4. F
mO = ____
3. G  ____
5. QO = ____
6. GFE ____
Examples - Write a congruence statement for the figures . Make sure to match up your letters correctly!
Transitive Property of Congruent Triangles
(2 things =to the same thing must be =to each other)
If ABC  DEF, and DEF  JKL, then ________________
Examples
In the diagram below, E is the midpoint of
Show that ABE  CDE.
AC and BD.
In the diagram, what is the measure of D?