AA SSS and SAS II 7 3 Triangle

AA, SSS, and SAS II 7 -3 Triangle Lesson 102: Similarity: Similar Triangle Proofs Explain why the triangles are similar and write a similarity statement. By the Triangle Angle Sum Theorem, m C = 47°, so C F (A). B E because all right angles are congruent (A). Therefore, ∆ABC ~ ∆DEF by AA ~ Theorem. Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS Take Out Last Night’s HW Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS Reteach Worksheet 6 -5, #6 Since the diagonals LM & NP have equal lengths of √ 26, they are congruent and LMNP is a rectangle. Since the slopes of diagonals LM (1/5) & NP (-5/1) are negative reciprocals (or multiply to -1), they are perpendicular and LMNP is a rhombus. Since LMNP is a rectangle and a rhombus, it is a square. *Make sure you have also shown the math* Holt Geometry

Page Triangle Similarity: AA, SSS, and SAS 7 -3 431 Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS 21. The triangles are similar by AA Theorem. 78 meters Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS Today, we are going to learn about 2 more shortcuts for proving triangles similar They involve proportional relationships or equal fractions Holt Geometry

The second. Similarity: shortcut is: AA, SSS, and SAS 7 -3 Triangle SSS is about BA =theorem AC = CB 3 EQUAL FRACTIONS ED DF FE Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS To prove triangles similar by the SSS Similarity Theorem, show that the 3 pairs of corresponding sides reduce to the same fraction. Holt Geometry

AA, SSS, and SAS 7 -3 Triangle Similarity: Proving Triangles Verify that the triangles are similar. ∆PQR and ∆STU When triangles are similar, the pairs of corresponding sides have the same similarity ratio ∆PQR ~ ∆STU by SSS ~ Theorem Holt Geometry

Triangle Similarity: 7 -3 third The shortcut is: AA, SSS, and SAS BA = CB isand B E of SAS Theorem a COMBINATION 2 equal and 1 pair of angles ED fractions FE Holt Geometry

7 -3 Triangle Similarity: AA, SSS, and SAS To prove triangles similar by the SAS Similarity Theorem, show that 2 pairs of corresponding sides reduce to the same fraction AND the pair of included angles are congruent Holt Geometry

Triangle Similar AA, by SAS ~ Theorem Triangle Similarity: SSS, and SAS 7 -3 Proving Verify that the triangles are similar. ∆DEF and ∆HJK D H (A) Same fraction means sides are proportional ∆DEF ~ ∆HJK by SAS ~ Theorem Holt Geometry

Similarity: 7 -3 Triangle Extra Practice (if time)AA, SSS, and SAS Verify that ∆TXU ~ ∆VXW. TXU VXW by the Vertical Angles Theorem. ∆TXU ~ ∆VXW by SAS ~ Theorem. Holt Geometry

Triangle Similarity: AA, SSS, and SAS 7 -3 HW #102 Big Ideas 441 - 443 Pages 1, 2 – 18 even, 19, 28 -31, 35, 36, 37, 39 Proof Sheet #4 Thinkthroughmath due Sundays by 11: 59 pm Holt Geometry