Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Penrose tiling wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Multilateration wikipedia , lookup
Technical drawing wikipedia , lookup
Apollonian network wikipedia , lookup
Rational trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Warm up… • checkpoint quiz page 429 #’s 1 – 10 8.3 Proving Triangles Similar SWBAT… • To use AA, SAS, and SSS similarity statements • To apply AA, SAS and SSS similarity statements. Investigation: triangles w/ 2 pairs of congruent angles • Use page 432 and complete the investigation in the blue box. • We’ll have a class discussion in 4 minutes. Angle – Angle Similarity (AA~) Postulate • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. S B R T A C If angles A and R are congruent and angles B and S are congruent (mark them), Then triangle ABC ~ triangle RST Example 1 • MX is perpendicular to AB. Explain why the triangles are similar. Write a similarity statement. M K B 58 58 X A Side Side Side Similarity • THEOREM: if the corresponding sides of two triangles are proportional, then the triangles are similar. S B R T A C Example 2 • If AB = 18, BC = 12, AC = 21, RS = 6, ST = 4, RT = 7 are the triangles similar? S B R T A C Side – Angle – Side (SAS ~) • If the measures of two sides are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. S B R A C T Example 3 S B 12 6 8 R A C Are the two triangles similar? 4 T Example 4 • In the figure AB || DC, CD DE , AB BE , BE 27, DE 45, AE 21, CE 35 Determine which triangles are similar. C B E A D Example 5 • Given UT || RS, find SQ and QU. U R 2x + 10 10 4 X+3 S T Example 6 • If you wanted to measure the height of the Sears tower in Chicago, you could measure a 12-foot light pole and measure its shadow. If the length of the shadow was 2 feet and the shadow of the Sears Tower was 242 feet, what is the height of the Sears Tower? Class work… • Page 435 – 436 #’s 1 – 19, 23, 45 – 48 • We do have a short quiz Monday on what we’ve covered in Ch. 8 • Chapter 8 test is Friday of next week.