Triangle Similarity: AA, SSS, SASTriangle Similarity: AA .
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.QX; RY; SZ;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, BE by the Alternate InteriorAngles Theorem. Also, AD 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 CBE by the Right Angle Congruence Theorem.Therefore, ABC DEF by AA .Holt McDougal GeometryF.
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 HJKDH 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.TXUVXW 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.AA by Reflexive Property of , andsince they are both right angles.Therefore ABE ACD by AA .Holt McDougal GeometryBC
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 ST.RR 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, 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
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
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
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.
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
Students use the AA similarity postulate, SSS similarity theorem, and SAS similarity theorem in order to prove the parallel segment proportionality theorem and triangle midsegment theorem. G.SRT.B.4 Triangle Congruence Introduction to Triangle Congruence Students practice writing and identifying triangle congruency statements,
Geometry Unit 2—Triangle Congruence Notes Triangle Congruence Theorems (SSS AND SAS) Practice: Mark the included side in each triangle Practice: Mark the included angle in each triangle. Side – Side – Side (SSS) Congruence Theorem Congruence Theorem three sides of one triangle are congr
Holt McDougal Geometry 4-5 Triangle Congruence: SSS and SAS In Lesson 4-3, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. The property of triangle rigiditygives you a shortcut for proving two triangles
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