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

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.

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.

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.

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

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

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

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

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