Quarter 2, Week 4: November 6th – 9th

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TeacherFelicia Taylor
Subject AreaGeometry Honors
Grade Level8th
Week #13
Unit of Instruction3: Similarity
Standard(s) Taught

MAFS.912.G-SRT.1.1
Verify experimentally the properties of dilations given by a center and a scale factor:
a. 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.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

MAFS.912.G-SRT.1.2
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.

MAFS.912.G-SRT.1.3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

MAFS.912.G-SRT.2.4
Prove theorems about triangles. (Theorems include: Triangle Proportionality Theorem or Side Splitter Theorem – a line parallel to one side of a triangle divides the other two proportionally.)

MAFS.912.G-SRT.2.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Learning Targets and Learning Criteria

• use dilations to prove similar figures.
• define dilation. (clarify that dilations are not rigid motions).
• use real-world applications of dilations.
• perform a dilation with a given center and scale factor on a figure in the coordinate plane.
• verify that when a side passes through the center of dilation, the side and its image lie on the same line.
• verify that corresponding sides of the pre-image and images are parallel.
• verify that a side length of the image is equal to the scale factor multiplied by the corresponding side length of the pre-image.

• define similarity as a composition of rigid motions followed by dilations in which angle measure is preserved and side length is proportional.
• identify corresponding sides and corresponding angles of similar triangles.
• demonstrate that in a pair of similar triangles, corresponding angles are congruent (angle measure is preserved) and corresponding sides are proportional.
• determine that two figures are similar by verifying that angle measure is preserved and corresponding sides are proportional.

• show and explain that when two angle measures are known (AA), the third angle measure is also known (Third Angle Theorem).
• conclude and explain that AA, SSS, and SAS similarity are sufficient conditions for two triangles to be similar.
• distinguish between congruence and similarity theorems.

• apply theorems, postulates, or definitions to prove theorems about triangles and proportional parts of parallel lines, including:
a) Triangle Proportionality Theorem- A line parallel to one side of a triangle divides the other two proportionally.
b) Converse of Proportionality Theorem- If a line divides two sides of a triangle proportionally, then it is parallel to the third side
c) Triangle Midsegment Theorem
( side splitter theorem as applied to triangle) – a midsegment of a triangle is parallel to one side of a triangle and its length is one-half the length of that side.

• use triangle similarity to solve problems
• use triangle similarity to prove relationships in geometric figures.

Classroom Activities

Geometry Nation Study Guides will only be distributed to Periods 7 & 8 since they do not have Geometry Nation Workbook.  Period 2 needs to bring Geometry Nation Workbook to every Geometry class.

Monday (2nd Period) / Tuesday (7th & 8th Periods)

Review the IXL assignments that are due:

  1.  L.16 Dilations and Parallel Lines – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)
  2. P.4 Side lengths and angle measures in similar figures – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)

Complete Geometry Nation Study Guides together in class:

  1.  Section 5, Topic 5:  Congruence and Similarity of Polygons – Part 2
  2. Section 7, Topic 1:  Triangle Similarity – Part 1

Homework:

IXL

  1. P.3 Identify similar figures – due Thursday, November 9th (2nd Period) / due Wednesday, November 15th (7th & 8th Periods)
  2. P.13 Prove proportions or angle congruences using similarity – due Thursday, November 9th (2nd Period) / due Wednesday, November 15th (7th & 8th Periods)

Wednesday (Short Class Periods – Early Release Day)

Classwork:

  1. Section 7, Topic 2:  Triangle Similarity – Part 2
  2. IXL – P.6 Perimeters of Similar Figures
  3. IXL – P.11 Areas of Similar Figures

Distribute Unit 2B/3 Test Study Guide.  Unit 2B/3 Practice test available on MathSpace.  

Homework (7th & 8th Periods only):

Geometry Nation:

  1. Section 4, Topic 8:  Dilations of Polygons

IXL

  1. P.8 Similar triangles and similarity transformations – due Wednesday, November 15th (7th & 8th Periods) 

Thursday (2nd Period only)

Complete Geometry Nation Study Guides together in class:

  1. Section 4, Topic 8:  Dilations of Polygons

Homework:

IXL

  1. P.8 Similar triangles and similarity transformations – due Monday, November 13th

Friday

NO SCHOOL

Assignments Due

Summative

None

Formative

IXL assignments:

  1. L.16 Dilations and Parallel Lines – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)
  2. P.4 Side lengths and angle measures in similar figures – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)
  3. P.6 Perimeters of similar figures – due Wednesday, November 8th (all classes)
  4. P.11 Areas of similar figures – due Wednesday, November 8th (all classes)
  5. P.3 Identify similar figures – due Thursday, November 9th (2nd Period)
  6. P.13 Prove proportions or angle congruences using similarity – due Thursday, November 9th (2nd Period)
Additional Resources

Please review Geometry Nation videos that correspond with topics covered in class if more help is needed.

www.khanacademy.com is also another good source of help.