CPCTC  ’s Naming  ’s Algebra Connection Proofs Altitudes & Medians 100 200 300 400 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200.

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Presentation transcript:

CPCTC  ’s Naming  ’s Algebra Connection Proofs Altitudes & Medians

CPCTC A B D EF C If  ABC   DEF, then  C   F.

CPCTC If  ABC   DEF, then  BCA   EFD

CPCTC If  JKL   ABC, name another way to state that the triangles are congruent.  KLJ   BCA  JLK   ACB  LJK   CAB  LKJ   CBA  KJL   BAC

CPCTC C D BA  ACB  DBC

CPCTC What does the acronym CPCTC stand for? Corresponding Parts of Congruent Triangles are Congruent.

Congruent Triangles Which method(s) can you use to prove that the given triangles are congruent? SSS C AB D  ABC   DCB

Congruent Triangles Which method(s) can you use to prove that the given triangles are congruent? A D F K L B  ABD   FKL HL

Congruent Triangles Which method(s) can you use to prove that the given triangles are congruent? L M NP SAS, AAS, ASA  LPN   NML

Congruent Triangles Which method(s) can you use to prove that the given triangles are congruent? B A D C  ABC   DCB SAS

Congruent Triangles Which method(s) can you use to prove that the given triangles are congruent? AC D B DB is a median and an altitude of  ADC.  ABD   CBD SAS

Naming Triangles K L J C B A  ABC  JKL

Naming Triangles H G K J  HJG  KJG

Naming Triangles DC BA  ABD  CDB

Naming Triangles  JKL  M J K L  LMJ

Naming Triangles  ABC  B A C D E F NONE! There is not sufficient evidence to conclude that the two triangles are congruent!

Algebra Connection x 3x - 14 Solve for x. x = 26

Algebra Connection x3x 4x x = 20 Solve for x.

Algebra Connection x + 126x + 2 y Solve for x and y. x = 10y = 56

Algebra Connection Solve for x and y. y x x 30  x = 75y = 105

Algebra Connection Find x. Classify this triangle by its sides and angles. Name the longest and shortest sides. 2x B C A Figure not drawn to scale. 7x - 2 4x x = 14 Sides: Scalene Angles: Obtuse Longest: AB Shortest: AC

Proofs Draw a logical conclusion from the given statement and state the reason. AB D Given: D is the midpoint of AB AD  DB because of the definition of a midpoint.

Proofs Draw a logical conclusion from the given statement and state the reason. A B C D Given: AC is the angle bisector of  BAD. 1.  BAC   CAD because of the definition of an angle bisector.

Proofs Draw a logical conclusion from the given statement and state the reason. BC D A Given: BD is an altitude of  ABC AC  BD because of the definition of an altitude.

Proofs A C D Given: BD bisects  ABC;  ADB   CDB Prove: AB  CB B BD bisects  ABC 1. Given  ABD   CBD Definition of an  bisector  ADB   CDBGiven BD  BDReflexive  ABD   CBDASA AB  CB CPCTC

Proofs Given: AC is a median. AB  AD Prove:  ABC   ADC StatementsReasons A B C D 1. AC is a median.1. Given C is the midpoint of BD. Definition of a median. BC  CDDef. of a midpoint. AB  AD Given AC  AC Reflexive  ABC   ADCSSS

Medians and Altitudes Name a median. A E D C B AD

Medians and Altitudes Name an altitude. A E D C B EB

Medians and Altitudes Identify BC as a median, altitude, perpendicular bisector, angle bisector or none of these. C B None of these.

Medians and Altitudes In which type of triangle do two of the altitudes lie on the outside of the triangle? An Obtuse Triangle.

Medians and Altitudes Identify BC as a median, altitude, perpendicular bisector, angle bisector or none of these. C B Median