Quarter 2, Week 4: November 6th – 9th

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Teacher Felicia Taylor Geometry Honors 8th 13 3: 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)