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11-16-12 Carmirlyta Despeignes wanise saintil

Study guide . 11-16-12 Carmirlyta Despeignes wanise saintil. Table of contents. 4.1 → 4.2 → 4.3 → 4.4 → 4.5 → 4.6 → 5.1 →. classifying triangles angles of triangles congruent triangles proving congruence-SSS,SAS Proving congruence ASA, AAS Isosceles triangles

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11-16-12 Carmirlyta Despeignes wanise saintil

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  1. Study guide 11-16-12Carmirlyta Despeigneswanise saintil

  2. Table of contents • 4.1 → • 4.2 → • 4.3 → • 4.4 → • 4.5 → • 4.6 → • 5.1 → • classifying triangles • angles of triangles • congruent triangles • proving congruence-SSS,SAS • Proving congruence ASA, AAS • Isosceles triangles • bisectors, medians, and altitudes

  3. 4.1 Classifying triangles Classifying triangles • Example I: find x, QR, RS, and QS if triangle QRS is an equilateral triangle. • 4x=2x+1 • 4x-2x=1 • 2x=1 • X=1/2 • Example II: find x and the measures of the unknown sides of each triangle. • 5x=3x+10 • 5x-3x=10 • 2x=10 • X=5 • 5(5) • 25 • 3(5)+10 • 25 • 6(5)-5 • 25 2x+1 4x 5x 6x-5 6x-1 3x+10

  4. 4.2 Angles of triangle Angles of triangle • Example I: find each measure if m<DGF = 52 and m<AGC = 40. • M<1= 90+ 53 • M<1=37 • M<2=90-40 • M<2= 50 • Example II: find each measure if m<DGF=52 and m<AGC =40. • M<3=90+40 • M<3=180-130 • M<3=50 • M<4=90-50 • M<4= 40

  5. 4.3 Congruent triangles Congruent triangles • Example I: identify the corresponding congruent angles. • AFC=DFB • <A=<D • <C=<B • BFD=CFA • AC=DB • AF=DF • FC=FB • Example II: • EFH=GHF • <e=<g • EHF=GFH • EF=GH • GF=FH D F C B

  6. 4.4 Proving congruence SSS, SAS or not possible Proving congruence SSS,SAS • Example I: • They are not possible • Figure of a rectangle cut in half • Example II: • If a triangle’s sides are congruent to the sides of a second triangle, the triangles are congruent. • Figure of two triangles

  7. 4.5 Proving congruence ASA, AAS Proving congruence ASA, AAS • Example I: • a) AAS • B) ASA • C) SAS • D) SSS • The answer is B because BC is perpendicular to AD. • Example 2: • If IR MV≈ MV, then triangle IRN ≈ triangle VMN, ASA OR AAS R I N B V M A D C

  8. 4.6 ISOSCELES TRAINGLES ISOSCELES TRIANGLES • Example I: • Find x and y • 3x+1=4x-2 • 3x-4x=-1-2 • -x=-3 • X=3 • 90=5y • Y=18 • Example II: triangle LMN is equalitateral, and MP bisects LN The measure of each side is 10. M 4x-2 4x-2 3x+1 3x+1 5y 5y L N P

  9. 5.1 Bisectors, Medians, and Altitudes Bisectors, Medians, and Altitudes • The vertices of triangle ABC are A(-3,3), B(3,2) and C(1,-4). Find the coordinates of the circumventer. • -17/38, -7/38 • Write two-column proof • Given: XY≈XZ • YM and ZN are medians • Proof: YM≈ZN • Statement • <xzy≈<xzy isosceles triangle theorem • Triangle MYZ≈ triangle SAS • NZY • Xy≈ XY, YM and ZN are Given • Median X M N Z Y

  10. Basically, what we were learning from this chapter are: How to classify the different type of triangles, Measure the sides of the triangles Assuming whether they are congruent or not How to classify different type of angles CONCLUSION

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