# Quarter 2, Week 3: October 30th – November 3rd

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Teacher Felicia Taylor Geometry Honors 8th 12 2B: Triangle Properties; 3: Similarity
Standard(s) Taught

MAFS.912.G-CO.3.10
Prove theorems about triangles; use theorems about triangles to solve problems. (Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.)
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.

Learning Targets and Learning Criteria

• 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.

• 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.

• solve problems using definitions, theorems, postulates, about triangles, including:
a) Hinge Theorem.
b) The medians of a triangle meet at a point.

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)

Complete Geometry Nation Study Guides together in class:

1. Section 7, Topic 6:  More Triangle Proofs
2. Section 7, Topic 8:  Medians in a Triangle
3. Section 4, Topic 1:  Introduction to Polygons – Part 1

Homework:

IXL

1. M.2 – Triangles and bisectors – due Thursday, November 2nd (2nd Period) / due Friday, November 3rd (7th & 8th Periods)
2. M.3 – Identify medians, altitudes, angle bisectors and perpendicular bisectors – due Monday, October 30th (2nd Period)/ due Tuesday, October 31st (7th & 8th Periods)

Wednesday (Short Class Periods – Early Release Day)

Complete Geometry Nation Study Guides together in class:

1.  Section 4, Topic 2:  Introduction to Polygons – Part 2

Work on IXL assignments from last week and/or Monday/Tuesday.

Homework:

No new homework assignments

Thursday (2nd Period) / Friday (7th & 8th Periods)

Complete the following Geometry Nation Study Guides together in class:

1. Section 4, Topic 8:  Dilations of Polygons
2. Section 5, Topic 4:  Congruence and Similarity of Polygons – Part 1

Homework:

IXL

1. L.16 – Dilations and Parallel Lines – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)
2. P.8 – Similar triangles and similarity transformations – due Monday, November 6th (2nd Period) / due Tuesday, November 7th (7th & 8th Periods)
Assignments Due

Summative

None

Formative

IXL assignments:

1. M.5 Triangle Inequality Theorem – due Monday, October 30th (2nd Period) / due Tuesday, October 31st (7th & 8th Periods)
2. M.8 Proofs involving triangles 1 – due Monday, October 30th (2nd Period) / due Tuesday, October 31st (7th & 8th Periods)
3. M.2 Triangles and bisectors – due Thursday, November 2nd (2nd Period) / due Friday, November 3rd (7th & 8th Periods)
4. M.3  Identify medians, altitudes, angle bisectors and perpendicular bisectors – due Thursday, November 2nd (2nd Period) / due Friday, November 3rd (7th & 8th Periods)

If students are still struggling with material please watch review the following:

1. IXL – M.1 Midsegment Theorem

Watch the following Geometry Nation Videos:

Section 7, Topic 3:  Triangle Midsegment Theorem – Part 1

Section 7, Topic 4:  Triangle Midsegment Theorem – Part 2

2. IXL – P.10 Triangle Proportionality Theorem

Review Unit 2(B) Triangle Properties Notes, page 1-2

3. IXL – M.5 Triangle Inequalities

Watch the following Geometry Nation video:

Section 7, Topic 5:  Triangle Inequalites

4. IXL – M.8 Proofs involving Triangles I

Watch the following Geometry Nation video:

Section 7, Topic 6:  More Triangle Proofs

5. IXL M.2 Triangles and bisectors

Watch the following Geometry Nation video:

Section 7, Topic 8:  Medians in a Triangle

6.  IXL M.3 Identify medians, altitudes, angle bisectors, and perpendicular bisectors

Watch the following Geometry Nation video:

Section 7, Topic 8:  Medians in a Triangle

7.  IXL L.16 Dilations and parallel lines

Watch the following Geometry Nation video:

Section 2, Topic 3:  Examining and using Dilations – Part 1

Section 2, Topic 4:  Examining and using Dilations – Part 2

Section 4, Topic 8:  Dilations of Polygons

8.  IXL P.8 Similar triangles and similar transformations

Watch the following Geometry Nation videos:

Section 5, Topic 4:  Congruence and Similarity of Polygons – Part 1