1. Lesson 4 – 3 Congruent Triangles
Geometry
Lesson 4 – 3
Congruent Triangles
Objective:
Name and use corresponding parts of congruent polygons.
Prove triangles congruent using the definition of congruence.

2. Congruent Congruent Are the following congruent?
Figures that have exactly the same shape and size
Are the following congruent?
Congruent, all same shape
and size
Not congruent, same shape,
but not the same size.

3. Congruent Polygons Congruent Polygons Corresponding parts
All parts are congruent (angles and sides)
Corresponding parts
Parts of the polygons that ‘match up’
Two polygons are congruent if and only if their corresponding parts are congruent.

4. Corresponding angles Congruence Statement Corresponding Sides
Have to be in matching order

5. Congruence Statement:
Show that the polygons are congruent by identifying all the congruent corresponding parts. Then write a congruence statement.
Congruence Statement:

6. If and only if
If two polygons are congruent, then their corresponding parts are congruent.
Corresponding parts of congruent triangles are congruent
Abbreviation: CPCTC
CPCTC can/will be used as a reason in proofs.
NEED TO KNOW!

7. Find the values of x and y.
Use your congruence statement
to match up parts.
8y – 5 = 99
8y = 104
y = 13
2y + x = 38.4
2(13) + x = 38.4
26 + x = 38.4
x = 12.4

8. Find the values of x and y.12
x = 12
2y – 1 = 24
2y = 25
y = 12.5

9. Theorem 4.3 Third Angle Theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent.

10. The planners of the Senior Banquet decide to fold dinner napkins using the Triangle Pocket Fold so that they can place a small gift in the pocket.

12. Theorem 4.4 Properties of Triangle Congruence
Reflexive
Symmetric
Transitive

13. Homework
Pg – 7 all, 10 – 20 E, 24, 58