# Quarter 1, Week 8: October 2nd – 6th

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Teacher Felicia Taylor Geometry Honors 8th 8 2A / Triangle Congruence and Proofs
Standard(s) Taught

MAFS.912.G-CO.1.2
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

MAFS.912.G-CO.1.3
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

MAFS.912.G-CO.1.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MAFS.912.G-CO.1.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

MAFS.912.G-CO.2.6
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

MAFS.912.G-CO.2.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

MAFS.912.G-CO.2.8
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.

Learning Targets and Learning Criteria

• draw transformations of reflections, rotations, translations, and combinations of these using graph paper, transparencies, and/or geometry software.
• find the coordinates for the image (output) of a figure when a transformation rule is applied to the pre-image (input).
• distinguish between transformations that are rigid and those that are not.

• describe and illustrate how a rectangle, parallelogram, and trapezoid are mapped onto themselves using transformations.
• calculate the number of lines of reflection symmetry and the degree of rotational symmetry of any regular polygon.

• define pre-image and image, and use correct notation (A vs. A’)
• construct a reflection, translation, and rotation.
• model the reflection definition by connecting any point on the pre-image to its corresponding point on the reflected image and describing the line segment’s relationship to the line of reflection.
• model the translation definition by connecting any point on the pre-image to its corresponding point on the translated image, and connecting a second point on the pre-image to its corresponding point on the translated image, and describing how the two segments are equal in length, point in the same direction, and are parallel.
• model the rotation definition by connecting the center of rotation to any point on the pre-image and to its corresponding point on the rotated image, and describing the measure of the angle formed and the equal measures of the segments that formed the angle as part of the definition.

• draw a specific transformation when given a geometric figure and a rotation, reflection, or translation.
• predict and verify the sequence of transformations (a composition) that will map a figure onto another.

• define and use rigid motions as reflections, rotations, translations and combinations of these, all of which preserve distance and angle measure.
• define congruent figures as figures that have the same shape and size and state that a composition of rigid motions will map one congruent figure onto the other.
• predict the composition of transformations that will map a figure onto a congruent figure.
• determine if two figures are congruent by determining if rigid motions will turn one figure into the other.

• identify corresponding sides and corresponding angles of congruent triangles.
• explain that in a pair of congruent triangles, corresponding sides are congruent (distance is preserved) and corresponding angles are congruent (angle measure is preserved).
• demonstrate that when distance is preserved (corresponding sides are congruent) and angle measure is preserved (corresponding angles are congruent) the triangles must also be congruent.

• list the conditions to prove triangles are congruent.
• map a triangle with one of the conditions (e.g., SSS) onto the original triangle and show that corresponding sides and corresponding angles are congruent.
• explain AAS as criterion for congruence, and demonstrate that SSA and AAA do not prove congruence.

Classroom Activities

Monday, October 2nd (2nd Period) / Tuesday, October 3rd (7th & 8th Periods)

Do Bellringer

Review Bellringer

Give Test Grades and Test Retake forms (No tests will be returned until all students have been tested.)

Lesson on Congruence Transformations – rigid motion only.  Students are to take notes.

Practice transformations on IXL (L.1) as a class.  Students are to take notes.

Classwork:  Do IXL L.3 – Translations , L.6 – Reflections , L.9 – Rotations

Homework is MathSpace assignment:  Transformations and Congruence due Thursday, October 5th (2nd Period) / Friday, October 6th (7th & 8th Periods).

Put away iPads and complete Exit ticket to leave class.

Wednesday, October 4th

Do Bellringer

Review Bellringer

Classwork:  Do IXL L.2 – Translations, L.5 – Reflections, L.8 – Rotations.  Grades (SmartScores) will be placed in GradeBook.

Put away iPads.  No Exit ticket today.

Thursday, October 5th (2nd Period) / Friday, October 6th (7th & 8th Periods)

Do Bellringer

Review Bellringer

Lecture:  Classifying Triangles, Proving Triangles Congruent – SSS, SAS, ASA, AAS

Practice learning about triangles and triangle proofs on IXL – K.1 & K.3 – SSS, SAS, ASA, AAS theorems

Homework is MathSpace assignment: Congruence in Triangles – due Monday, October 9th (2nd Period) / Tuesday, October 10th (7th & 8th Periods).

Put away iPads and complete Exit ticket to leave class.

Assignments Due
1. Bellringers – due 10 minutes after the start of class.
2. IXL
1. L.2 – Translations: graph the image – due Wednesday, October 4th
2. L.5 – Reflections: graph the image – due Wednesday, October 4th
3. L.8 – Rotations: graph the image – due Wednesday, October 4th
3. MathSpace
1. Transformations and Congruence – due Thursday, October 5th (2nd Period) / due Friday, October 6th (7th & 8th Periods)

Congruence Transformations

If still confused or need further instruction on Congruence Transformations, please watch the following on Geometry Nation:

Section 2, Topic 1:  Introductions to Transformations

Section 4, Topic 4: Translation of Polygons

Section 4, Topic 5: Reflection of Polygons

Section 4, Topic 6: Rotation of Polygons-Part 1

Triangles and Triangle Congruence

If still confused or need further instruction about Triangles and Triangle Congruence, please watch the following on Geometry Nation:

Section 6, Topic 1:  Introduction to Triangles – Part 1

Section 6, Topic 2:  Introduction to Triangles – Part 2

Section 6, Topic 5: Triangle Congruence – SSS and SAS – Part 1

Section 6, Topic 6: Triangle Congruence – SSS and SAS – Part 2

Section 6, Topic 7: Triangle Congruence – ASA and AAS – Part 1

Section 6, Topic 8: Triangle Congruence – ASA and AAS – Part 2