16 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.x to y
17 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.2 to 3
18 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.6x2 to 12xy
19 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.1 to 3
20 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.y – xx
21 White Board Practicex = 2 and y = 3. Write each ratio in simplest form.12
22 7.2 Properties of Proportions ObjectivesExpress a given proportion in an equivalent form.
23 Means and Extremes a b c d a : b = c : d The extremes of a proportion are the first and last termsThe means of a proportion are the middle termsThe role of the extremes and means is to make the manipulations learned today easier to describe.=abcda : b = c : d
24 Properties of Proportion is equivalent to1.2.3.Each of these is a different property.4.
25 That just means that you can rewrite As any of these1.2.3.Each of these is a different property.4.
26 Another PropertySelect and work several example problems off of the classroom exercises.
35 7.3 Similar Polygons Objectives State and apply the properties of similar polygons.
36 Similar PolygonsSame shapeNot the same size Why?
37 Because then they would be congruent ! Not the same size Why?Because then they would be congruent !
38 Similar Polygons (~) All corresponding angles congruent A A’ B B’C C’AA’Write the extended proportion and the congruencies on the diagram.CBB’C’
39 Similar Polygons (~) All corresponding sides in proportion AB = BC = CAA’B’ B’C’ C’A’AA’Write the extended proportion and the congruencies on the diagram.BCB’C’
40 The Scale FactorThe reduced ratio between any pair of corresponding sides or the perimeters.12:312Work several examples of how to find the scale factor, and how to use it to find the unknown parts.3
41 Finding Missing Pieces You have to know the scale factor first to find missing pieces.12Work several examples of how to find the scale factor, and how to use it to find the unknown parts.310y
42 White Board PracticeQuadrilateral ABCD ~ Quadrilateral A’B’C’D’. Find their scale factorADCBA’D’C’B’50y302012xz
48 7.4 A Postulate for Similar Triangles ObjectivesLearn to prove triangles are similar.
49 AA Simliarity Postulate (AA~ Post) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.ADThis can be shown to prove triangles similar, although there is no proof of it. Why are the sides of a triangle in proportional if the angles are congruent? Do a proof using this postulate.FEBC
50 Remote TimeT – Similar TrianglesF – Not Similar
55 7-5: Theorems for Similar Triangles ObjectivesMore ways to prove triangles are similar.
56 SAS Similarity Theorem (SAS~) If an angle of a triangle is congruent to an angle of another triangle and the sides including those angles are proportional, then the triangles are similar.ADThis is a difficult theorem to prove, so it is not wise to prove it in class, unless it is an honors group. Do a proof that uses it, however. Also talk about how this makes the triangles “almost” congruent. Compare the SAS, the SAS and the SAS.FEBC
57 SSS Similarity Theorem (SSS~) If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.ADDitto.FEBC
59 7-6: Proportional Lengths ObjectivesApply the Triangle Proportionality Theorem and its corollaryState and apply the Triangle Angle-bisector Theorem
60 Divided Proportionally If points are placed on segments AB and CD so that , then we say that thesesegments are divided proportionally.BThis just gets them comfortable with the idea of divided proportionally. Show them several correct proportions that can be written. Also show them an incorrect proportion and why it is incorrect. Most of these are intuitive.DXYACSee It!
61 Theorem 7-3If a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally.YSee It!Ditto.BAXZ
62 CorollaryIf three parallel lines intersect two transversals, they they divide the transversal proportionally.RWSXDitto.TYSee It!
63 Theorem 7-4If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.YSee It!Ditto.WXZ
64 Construction 12Given a segment, divide the segment into a given number of congruent segments.Given:Construct:Steps:Do the construction for them on the board. The steps are in the textbook, and can be written down later.
65 Construction 13Given three segments, construct a fourth segment so that the four segments are proportional.Given:Construct:Steps:Do the construction for them on the board. The steps are in the textbook, and can be written down later.
66 Homework Set 7.6 WS PM 41 WS Constructions 12 and 13 7-6 #1-23 odd Quiz next class day