1. Congruent Triangles. Congruence Postulates.
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Congruent Triangles. Congruence Postulates.
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

2. FG, GH, FH, F, G, H Warm Up 1. Name all sides and angles of ∆FGH.
2. What is true about K and L? Why?
3. What does it mean for two segments to be congruent?
FG, GH, FH, F, G, H
 ;Third s Thm.
They have the same length.

3. Objectives 1.Use properties of congruent triangles.
Prove triangles congruent by using the definition of congruence.
2. Apply SSS and SAS to construct triangles and solve problems.
3. Prove triangles congruent by using SSS and SAS.
4. Apply ASA, AAS, and HL to construct triangles and to solve problems.
5. Prove triangles congruent by using ASA, AAS.

4. corresponding angles corresponding sides congruent polygons SSS SAS
Vocabulary
corresponding angles
corresponding sides
congruent polygons
SSS SAS
ASA AAS
included angle
included side
CPCTC

5. Geometric figures are congruent if they are the same size and shape
Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides.
Two polygons are congruent polygons if and only if their corresponding sides are congruent. Thus triangles that are the same size and shape are congruent.

7. For example, P and Q are consecutive vertices.
Two vertices that are the endpoints of a side are called consecutive vertices.
For example, P and Q are consecutive vertices.
Helpful Hint

8. To name a polygon, write the vertices in consecutive order
To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.
In a congruence statement, the order of the vertices indicates the corresponding parts.

9. When you write a statement such as ABC  DEF, you are also stating which parts are congruent.
Helpful Hint

10. Triangle Congruence Postulates
Adjacent triangles share a side, so you can apply the Reflexive Property to get a pair of congruent parts.
Remember!

11. Example 1: Using SSS to Prove Triangle Congruence
Use SSS to explain why ∆ABC  ∆DBC.
It is given that AC  DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

12. An included angle is an angle formed by two adjacent sides of a polygon.
B is the included angle between sides AB and BC.

13. Triangle Congruence Postulates
The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides.
Caution

14. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

16. You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

18. CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

19. SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent.
Remember!