(4.4) CPCTC Corresponding Parts of Congruent Triangles Congruent

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4-4 Using Congruent Triangles: CPCTC

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Presentation transcript:

(4.4) CPCTC Corresponding Parts of Congruent Triangles Congruent

Proving Triangles Congruent LT: To use triangle congruence and CPCTC to prove that parts of two triangles are congruent. Relevancy: This concept of CPCTC can be used measure distance indirectly.

Proving Triangles Congruent Can we use (SSS, SAS, AAS, or ASA) the given information to prove triangles congruent? Not Possible ASA AAS SSS Seriously?  SAS 3

Proving Triangles Congruent D B C E A Given Look For… Reason Example Two segments are congruent Midpoint Defn. of midpoint Segment bisects a segment Two segments are congruent Defn. of bisector Two segments parallel Alt. int. angles congruent Alt. int. angles theorem Vertical angles Two congruent angles Vert. angles theorem

Proving Triangles Congruent X 1 2 W Z Y Given Look For… Reason Example Segment bisects an angle Two angles are congruent Defn. of angle bisector Triangles that share a side A segment congruent to itself Reflexive property of congruence Perpendicular segments Two angles are congruent 1) Right angles by defn. of lines 2) All right angles

Proving Triangles Congruent With SSS, SAS, ASA, and AAS; you know how to use three parts of triangles to show that the triangles are congruent. Once you have triangles congruent, you can make conclusions about their other parts because by definition, Corresponding Parts of Congruent Triangles are Congruent (CPCTC) **You can use CPCTC in a proof. 6

Proving Triangles Congruent X W Z Y Statement Reason 1. Given 2. 2. Given 3. Defn. of Angle Bisector 4. Right angles are congruent because of defn. of perpendicular lines 5. Reflexive Property of ≌ 6. 6. ASA

Proving Triangles Congruent B C E A D Statement Reason 1. 1. Given 2. Defn. of Midpoint 3. 3. Vertical Angles 4. 4. SAS 5. 5. CPCTC

homework Sticker #3 Due: Wed. 1/29 Sticker #4 Due: Fri. 1/31 Practice WS (4.4) Due: Wed. 1/29 Study Island Challenge Due: Wed. 3/12 Update 3 x 5 Cards