COMMON CORE OBJECTIVES G.SRT.A.1 TO G.SRT.A.3

G.SRT.A.1A Verify experimentally the properties of dilations given by a center and a scale factor: a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

 

G.SRT.A.1B Verify experimentally the properties of dilations given by a center and a scale factor: the dilation of a line segment is longer or shorter in the ratio given by the scale factor.


G.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.


G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

 

COMMON CORE OBJECTIVES G.SRT.B.4 TO G.SRT.C.6

G.SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.


G.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures


G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

 

COMMON CORE OBJECTIVES G.SRT.C.7 TO G.SRT.C.8

G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.


G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard)

COMMON CORE OBJECTIVES G.SRT.D.9 TO G.SRT.D.11

HONORS ONLY

 

G.SRT.D. Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

 

G.SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems.


G.SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).


 


   

(1) In G.CO.A.2 we discussed isometric transformations and non-isometric transformations and there we introduced dilation.  This week is about really about exploring the dilation transformation -- its properties, graphing, determining scale factors, looking at different centers and applying dilations to real world situations. Dilations are the transformation that sets the stage for our exploration of similarity. This week lays a very important foundation.

(2) We begin to transition from the dilation properties and graphing to connecting that to similarity and what it means to be similar.  We introduce a new group of transformations – the similarity transformations of Reflection, Rotation, Translation, and Dilation.  A similarity transformation preserves the shape, which means proportionality of sides and congruence of angles.

 

Two figures are similar if and only if one can be obtained from the other by a single or sequence of similarity transformations.

 

(3) In this week we establish the minimum criteria  for similarity (AA, SAS & SSS) and then begin proving triangles to be similar.  We also prove two triangles to be similar so that we can talk about angle congruence and proportionality of sides.  We will use similarity to establish two new relationships the Side Splitting Theorem and the Angle Bisector Theorem.

(4) In this week we apply similarity to right triangles and investigate the geometric mean and special right triangle relationships.  Both of these relationships lead us nicely into trigonometry.

(5) In this week introduce the relationship between similarity and trigonometry.   Using similar triangles we will determine the ratios of sides and compare them to build the conceptual understanding of trigonometry.  From there we will study patterns found in these ratios.  One of the many patterns that we will discuss will be the relationship between sine and cosine as co-functions.

(6) We extend our knowledge of trigonometry by applying the ratios to problems in multiple environments.  We will apply the terms of angle of elevation and depression and other specific descriptors to help students establish the relationships in simplified ‘real world’ problems.

(7) HONORS ONLY – In this week we begin to look at how the sine ratio helps us determine lengths and angles in oblique triangles. We will derive the relationship and then apply them in multiple situations.  One of the major discussions will be the ambiguous case of the Law of Sines.

(8) HONORS ONLY– Finally we look at the Cosine Law and the cases that it handles so that we can solve for values of all oblique triangles. We will apply the Law of Sines and Cosines to simplified 'real world' problems.
 
  To revise this timeline for a regular geometry class you do not need to teach G.SRT.9, G.SRT.10 and G.SRT.11. This provides you with two weeks to extend the current timline... some topics such as geometric mean, special right triangles and trigonometry could easily be extended.