Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 4.1 Congruent Figures Congruent Figures: Have the same size and
Document related concepts
Dessin d'enfant wikipedia , lookup
Technical drawing wikipedia , lookup
Multilateration wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
4.1 Congruent Figures Congruent Figures: Have the same size and shape Corresponding sides and corresponding angles are congruent Congruence Statements: For the two congruent triangles, we can write the following: ∆ABC ≅ ∆FED or ∆BCA ≅ ∆EDF or ∆CAB ≅ ∆DFE (Note: Must be written in correct order!!) Corresponding angles: ∠A ≅ ∠F ∠B ≅ ∠E ∠C ≅ ∠D Corresponding sides: ̅̅̅̅ ̅̅̅̅ ≅ ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝐹𝐸 𝐵𝐶 𝐸𝐷 ̅̅̅̅ 𝐶𝐴 ≅ ̅̅̅̅ 𝐷𝐹 Yes (3rd angles theorem and reflexive prop) (Order matters!!) No (Corresponding sides are not congruent) X + 10 = 2x 3z + 2 = z + 6 x = 10 m<A and m<D = 20 2z = 4 z=2 BC and EF = 8 4.2 Triangle Congruence by SSS and SAS Statements FJ congruent to HJ G is mdpt FH FG congruent to GH JG congruent to JG ∆FGJ congruent to ∆HGJ Reasons Given Given Def midpt Reflexive SSS Congruence SSS, SAS, or not enough info? 4.3 Triangle Congruence by ASA and AAS Statements Reasons < B and <D are right angles Given ̅̅̅̅ ̅̅̅̅ 𝐴𝐸 bisects 𝐵𝐷 Given <B ≅ <D Right angles are ≅ <BCA ≅ <DCE Vertical angles ̅̅̅̅ ̅̅̅̅̅̅̅̅ 𝐵𝐶 ≅ 𝐷𝐶 Definition of bisector ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶 ASA AAS Not enough info ASA SAS 4.4 Using Corresponding Parts of Congruent Triangles What is the definition of congruent triangles? Corresponding parts of congruent triangles are congruent. (CPCTC) Why are they congruent? SAS What else can we conclude? ̅̅̅̅ ≅ 𝐷𝐹 ̅̅̅̅ < A ≅ <D, <C ≅ <F 𝐴𝐶 Statements Reasons ̅̅̅̅ , ̅̅̅ ̅̅̅ 𝐽𝐾 ‖𝑄𝑃 𝐽𝐾 ≅ ̅̅̅̅ 𝑃𝑄 Given <J ≅ <P Alternate Interior Angles <KMJ ≅ <QMP Vertical Angles ∆𝐾𝑀𝐽 ≅ ∆QMP AAS ̅̅̅̅ 𝐽𝑀 ≅ ̅̅̅̅̅ 𝑃𝑀 CPCTC M is a midpoint Def. of midpoint ̅̅̅̅ bisects ̅̅̅ 𝐾𝑄 𝐽𝑃 Def. of segment bisector 4.5 Isosceles and Equilateral Triangles Isosceles Triangle: A triangle with 2 congruent sides ̅̅̅̅ and 𝐵𝐶 ̅̅̅̅ Legs: 𝐴𝐶 Vertex angle: ∠C ̅̅̅̅ Base: 𝐴𝐵 Base angles: ∠A and ∠B 70 75 x = 40 y = 70 X = 60 y = 120 4.6 Congruence in Right Triangles Right Triangle: Statements ̅̅̅̅ 𝑄𝑆 ≅ ̅̅̅̅ 𝑃𝑅 Reasons ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ 𝑃𝑆 ̅̅̅̅ 𝑅𝑆 , 𝑄𝑅 𝑅𝑆 Given <S and < R are right angle Def. of Perpendicular ∆PRS and ∆QSR are right ∆′𝑠 Def. of right ∆ ̅̅̅̅ 𝑅𝑆 ≅ ̅̅̅̅ 𝑅𝑆 Reflexive Prop. ∆PRS ≅ ∆QSR HL
