77-3-3 Triangle Similarity: AA, SSS, SAS
SAS7-3 TriangleWarm UpLesson PresentationLesson ometry
7-3 Triangle Similarity: AA, SSS, SASWarm UpSolve each proportion.1.2.3.z 10x 84. If QRS XYZ, identify the pairs of congruentangles and write 3 proportions using pairs ofcorresponding sides. Q X; R Y; S Z;Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASObjectivesProve certain triangles are similar byusing AA, SSS, and SAS.Use triangle similarity to solve problems.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASThere are several ways to prove certain triangles aresimilar. The following postulate, as well as the SSSand SAS Similarity Theorems, will be used in proofsjust as SSS, SAS, ASA, HL, and AAS were used toprove triangles congruent.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 1: Using the AA Similarity PostulateExplain why the trianglesare similar and write asimilarity statement.Since, B E by the Alternate InteriorAngles Theorem. Also, A D by the Right AngleCongruence Theorem. Therefore ABC DEC byAA .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 1Explain why the trianglesare similar and write asimilarity statement.By the Triangle Sum Theorem, m C 47 , so C F. B E by the Right Angle Congruence Theorem.Therefore, ABC DEF by AA .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASHolt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASHolt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 2A: Verifying Triangle SimilarityVerify that the triangles are similar. PQR and STUTherefore PQR STU by SSS .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 2B: Verifying Triangle SimilarityVerify that the triangles are similar. DEF and HJK D H by the Definition of Congruent Angles.Therefore DEF HJK by SAS .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 2Verify that TXU VXW. TXU VXW by theVertical Angles Theorem.Therefore TXU VXW by SAS .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 3: Finding Lengths in Similar TrianglesExplain why ABE ACD, andthen find CD.Step 1 Prove triangles are similar. A A by Reflexive Property of , and B Csince they are both right angles.Therefore ABE ACD by AA .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 3 ContinuedStep 2 Find CD.Corr. sides are proportional.Seg. Add. Postulate.x(9) 5(3 9)9x 60Substitute x for CD, 5 for BE,3 for CB, and 9 for BA.Cross Products Prop.Simplify.Divide both sides by 9.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 3Explain why RSV RTUand then find RT.Step 1 Prove triangles are similar.It is given that S T. R R by Reflexive Property of .Therefore RSV RTU by AA .Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 3 ContinuedStep 2 Find RT.Corr. sides are proportional.Substitute RS for 10, 12 forTU, 8 for SV.RT(8) 10(12) Cross Products Prop.8RT 120RT 15Holt McDougal GeometrySimplify.Divide both sides by 8.
7-3 Triangle Similarity: AA, SSS, SASExample 4: Writing Proofs with Similar TrianglesGiven: 3UT 5RT and 3VT 5STProve: UVT RSTHolt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 4 ContinuedStatementsReasons1. 3UT 5RT1. Given2.2. Divide both sides by 3RT.3. 3VT 5ST3. Given.4.4. Divide both sides by3ST.5. RTS VTU5. Vert. s Thm.6. UVT RST6. SAS Holt McDougal GeometrySteps 2, 4, 5
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 4Given: M is the midpoint of JK. N is themidpoint of KL, and P is the midpoint of JL.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 4 ContinuedStatementsReasons1. M is the mdpt. of JK,N is the mdpt. of KL,and P is the mdpt. of JL.1. Given2.2. Midsegs. Thm3.3. Div. Prop. of .4. JKL NPM4. SSS Step 3Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASExample 5: Engineering ApplicationThe photo shows a gable roof. AC FG. ABC FBG. Find BA to the nearest tenthof a foot.From p. 473, BF 4.6 ft.BA BF FA 6.3 17 23.3 ftTherefore, BA 23.3 ft.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASCheck It Out! Example 5What if ? If AB 4x, AC 5x, and BF 4, find FG.Corr. sides are proportional.Substitute given quantities.4x(FG) 4(5x) Cross Prod. Prop.FG 5Holt McDougal GeometrySimplify.
7-3 Triangle Similarity: AA, SSS, SASYou learned in Chapter 2 that the Reflexive,Symmetric, and Transitive Properties of Equalityhave corresponding properties of congruence.These properties also hold true for similarity oftriangles.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASLesson Quiz1. Explain why the triangles aresimilar and write a similaritystatement.2. Explain why the triangles aresimilar, then find BE and CD.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SASLesson Quiz1. By the Isosc. Thm., A C, so by the def.of , m C m A. Thus m C 70 by subst.By the Sum Thm., m B 40 . Apply theIsosc. Thm. and the Sum Thm. to PQR.m R m P 70 . So by the def. of , A P,and C R. Therefore ABC PQR by AA .2. A A by the Reflex. Prop. of . Since BE CD, ABE ACD by the Corr. s Post.Therefore ABE ACD by AA . BE 4 andCD 10.Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SAS There are several ways to prove certain triangles are similar. The following postulate, as well as the SSS and SAS Similarity Theorems, will be used in proofs just as SSS, SAS, ASA, HL, and AAS were used to prove triangles congruent.
5. I can use the AA Similarity Postulate to prove triangle similarity 6. I can use the SSS Similarity Theorem to prove triangle similarity 7. I can use the SAS Similarity Theorem to prove triangle similarity 8. I can use proportion theorems to find missing lengths in geometric problems 9. I can perform dilations
(ii) Kinematic similarity: geometric similarity and similarity of motion between model and prototype particles (iii) Dynamic similarity: requires geometric and kinematic similarity and in addition that all force ratios in the two systems are identical Perfect model-prototype similarity: Mechanical similarity 8 . 5 Similarities Most relevant forces in fluid dynamics are: Inertial force mass .
The triangle has three acute angles that are not all equal. It is an acute triangle. 62/87,21 One angle of the triangle measures 90, so it is a right angle. Since the triangle has a right angle, it is a right triangle. 62/87,21 Since all the angles are congruent, it is a equiangular triangle. 62/87,21 The triangle
acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle Vocabulary. Holt McDougal Geometry 4-2 Classifying Triangles Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in
So, ADÆis a median of the triangle. The three medians of a triangle are concurrent. The point of concurrency is called the The centroid, labeled Pin the diagrams below, is always inside the triangle. acute triangle right triangle obtuse triangle The medians of a triangle have a special concurrency property, as described in Theorem 5.7.File Size: 695KBPage Count: 7
Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems. Objectives. Holt McDougal Geometry 7-3 Triangle Similarity: AA, SSS, SAS There are several ways to prove certain triangles are similar. The following postulate, as well as the SSS
Similarity: similar vs. congruent polygons, similarity postulates/theorems: AA, SSS, SAS, similar polygon perimeters (have the same scale factor as corresponding sides) Other similarity theorems: o Triangle Proportionality Theorem (and converse): line is to one side of a triangle IFF it intersects the other 2 sides proportionally
One final way to prove triangle similarity is the SAS Similarity Theorem. You will notice that it is similar to one of the congruence postulates you have learned about. Theorem 46-2: SAS Similarity Theorem - If two sides of one triangle are proportional to two sides of
