Homework

Similarity & Dilations

https://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/m2_mod6_se_52017f.pdf

Homework for November 5: p. 9-12 (questions 1-18)

Homework for November 7: p. 18-19 (questions 1-21)

Dilations Notes

Definition of Dilation - a transformation that moves points along a ray beginning at the center of dilation. These points are moved by finding the distance from the center of dilation and multiplying by a scale factor.

Properties of Dilations

1) Angles remain congruent.

2) The distance between the center of dilation and any point on the image is equal to the scale factor multiplied by the distance between the center of dilation and the corresponding point on the pre-image.

3) If a line intersects the center of dilation, the image of the line will be on the same line. When a line does not pass through the center of dilation, the image of the line segment will be parallel to the pre-image.

Study for Congruence & Similarity

Things to know for your SIMILARITY assessment:

• Congruence
  • Definition 1) Two figures are congruent if you can use translations, rotations, and reflections to get from the pre-image to the image.
  • Definition 2) Two figures are congruent if the corresponding angles are congruent and the corresponding sides are congruent.
• Similarity
  • Definition 1) Two figures are similar if you can use translations, rotations, reflections, AND dilations to get from the pre-image to the image.
  • Definition 2) Two figures are similar if the corresponding angles are congruent and the corresponding sides are proportional.
• Definition AND Properties of Dilations (above).
• How to find the measure of a missing side length (AND solve for x in an equation).
• How to find the center of dilation.
• How to find the scale factor of a dilation.
• How to prove if two figures are similar (AA, SAS, SSS, AAA Similarity Theorems).
• How to write similar triangles using the correct order of the vertices.
• Vertical Angles, Corresponding Angles, Alternate Interior Angles.

Things to know for your CONGRUENCE assessment:

• Congruence
  • Definition 1) Two figures are congruent if you can use translations, rotations, and reflections to get from the pre-image to the image.
  • Definition 2) Two figures are congruent if the corresponding angles are congruent and the corresponding sides are congruent.
• How to read congruence markings on a triangle.
• Theorems to prove triangles are congruent (SSS, SAS, AAS, ASA, HL - NOT AAA, SSA)
• How to prove triangles are congruent.
• Vertical Angles, Corresponding Angles, Alternate Interior Angles.

Similarity Stations and Key from 11/8/18

Congruence Study Guide Key distributed on 11/6/18

Examples of Triangle Congruence Proofs distributed on 11/6/18

You can do these several ways. Start by marking what is given on the triangles and anything else that you can mark.

Study Guide for Congruence Quiz