# Quarter 2, Week 5: November 13th – 17th

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Teacher Felicia Taylor Geometry Honors 8th 14 2B: Triangle Properties; 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

Monday (2nd Period)

Unit 2B/3 Test

If there is time after the test, students will finish incomplete/missing/late homework assignments.

Homework:

None

Tuesday (7th & 8th Periods)

Most of the students will be away at the 8th Grade Field Trip.  For the students who are at school, we will review for Unit 2B/3 test.

If there is time after the test review, students will finish incomplete/missing/late homework assignments.

Homework:

None

Wednesday (Early Release Day – Short Class Periods)

Go over the Unit 2B/3 test with 2nd period.

Unit 2B/3 Test for 7th and 8th periods.

Homework:

None

Thursday/Friday

Unit 3 DIA

If there is time after the DIA, have students complete missing/late/incomplete homework assignments.

Go over Flight project that 8th graders will be participating in next week.

Homework:

None

Assignments Due

Summative

Unit 2B/3 Test – on Monday, November 13th (2nd Period); on Wednesday, November 15th (7th & 8th Periods)

Formatives

Unit 3 DIA – due Thursday, November 16th (2nd Period); due Friday, November 17th

IXL

1. P.8 Similar triangles and similarity transformations – due Monday, November 13th (2nd Period); due Wednesday, November 15th (7th & 8th Periods)
2. P.3 Identify similar figures – due Wednesday, November 15th (7th & 8th Periods)
3. P.13 Prove proportions or angle congruences using similarity – due Wednesday, November 15th (7th & 8th Periods)