1. Pearson Unit 1 Topic 4: Congruent Triangles 4-4: Using Corresponding Parts of Congruent Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

2. TEKS Focus:
(6)(B) Prove two triangles are congruent by applying the Side-Angle-Side, Angle- Side-Angle, Side-Side-Side, Angle- Angle-Side, and Hypotenuse-Leg congruence conditions.
(1)(G) Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

4. 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.

5. 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.

6. 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. P Q R S

7. Example: 1 5 meters, by using CPCTC
Some hikers come to a river in the woods. They
want to cross the river but decide to find out how
wide it is first. So they set up congruent right
triangles. The figure shows the river and the
triangles. Find the width of the river, GH. Explain.
5 meters, by using CPCTC

8. Example: 2 Use the diagram to prove the following. 1. BA  DA 1. Given
STATEMENT
REASON
1. BA  DA
1. Given
2. CAB  EAD
2. Vertical Angle Theorem
3. CA  EA
3. Given
4. BAC  DAE
4. SAS
5. C E
5. CPCTC

9. Example 3: STATEMENT REASON 1. AB  AC 1. Given
2. M is the midpoint of BC
2. Given
2. BM  MC
2. Definition of Midpoint
3. AM  AM
3. Reflexive Prop. of Congruence
4. AMB  AMC
4. SSS
5. AMB  AMC
5. CPCTC

10. Example 4: STATEMENT REASON 1. KN and LM bisect each other 1. Given
2. KH  HN and LH  HM
2. Definition of Segment Bisector
3. KHL   NHM
3. Vertical Angle Theorem
4. KHL  NHM
4. SAS
5. KLH  NMH
5. CPCTC
6. KL || MN
6. Converse of Alternate Interior Angles Theorem