Lesson 60 Using Triangles 4 6 Triangle Congruence

Lesson 60 Using Triangles 4 -6 Triangle Congruence: CPCTC DO NOW: Take out yesterday’s proofs Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given 2. Converse of Base Angles Theorem 3. Subtraction Postulate 4. Substitution Postulate 5. Perpendicular lines intersect to form right angles. 6. All right angles are congruent. Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given TV Holt Geometry 2. Addition Postulate 3. Substitution Postulate

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given 2. A midpoint divides a segment into two congruent segments. 3. Substitution (or Transitive) Postulate Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given ’s. Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given 2. A median is drawn from a vertex of a triangle to the midpoint of its opposite side. 3. A midpoint divides a segment into two congruent segments. 4. Subtraction Postulate 5. Substitution Postulate 6. Base Angles Theorem Holt Geometry

proof for #6, using SSS Triangle Congruence: CPCTC 4 -6 Alternate Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given 2. A median is drawn from a vertex of a triangle to the midpoint of its opposite side. 3. A midpoint divides a segment into two congruent segments. 4. Subtraction Postulate 5. Substitution Postulate 6. Reflexive Postulate Holt Geometry

4 -6 Triangle Congruence: CPCTC Holt Geometry

4 -6 Triangle Congruence: CPCTC Statement Reason 1. Given 2. Perpendicular lines intersect to form right angles. 3. All right angles are congruent. 4. Alternate Interior Angles Theorem Holt Geometry

CPCTC 4 -6 Triangle Congruence: CPCTC ABC DEF A D C B E F What do you know about the 2 triangles pictured? Holt Geometry

CPCTC 4 -6 Triangle Congruence: CPCTC is an abbreviation for the phrase ”Corresponding Parts of Congruent Triangles are Congruent. ” It is usually used as a justification in a proof after you have proven two triangles congruent. Once it has been established that 2 triangles are congruent, it may be stated that any pair of corresponding parts in those 2 triangles are also congruent. Holt Geometry

CPCTC 4 -6 Triangle Congruence: CPCTC Given: AB CD and AD BC Prove: BAD BCD. A B Statement 1) AB CD, Reason 1) Given AD BC (s)(s) D Holt Geometry C 2) BD (s) 2) Reflexive Post. 3) BAD BCD 3) SSS 4) BAD BCD 4) CPCTC

CPCTC 4 -6 Triangle Congruence: CPCTC B Statement 34 1) BD Bisects ABC 1) Given 1 A Reason 2 D P: AD CD Holt Geometry 2) an angle bisector divides an angle into 2 angles 3) BD AC 3) Given 4) 1 & 2 are 4) lines form right ’s C G: BD bisects ABC BD AC 2) 3 4 (a) right ‘s 5) 1 2 (a) 5) right angles are 6) BD (s) 6) Reflexive Postulate 7) ABD CBD 7) ASA 8) AD CD 8) CPCTC

CPCTC 4 -6 Triangle Congruence: CPCTC HW #60 Text page 281 -282/#1, 3, 4, 6 -8 & HW 60 Worksheet Holt Geometry