Notes Date 2/13/19 NO Task, Grab your binder if you want Copy down the EQ Work on Warm Up Essential question Given two congruent triangles, how can you use rigid motions to map one triangle to the other triangle? Warm up: Describe each of the transformation in your own words. Translation Reflection Rotation

Purpose In this task students will apply rigid motion transformation to show how two shapes are congruent to each other. In the process, students will inquiry what corresponding parts come out from both shapes.

Understanding Rigid motion Transformations Two geometric figures are congruent if and only if a rigid motion or a composition of rigid motions maps one of the figures onto the other.

Determine the pre-image shape is congruent to the image Determine the pre-image shape is congruent to the image. Explain your answer Translation The length and angles remain the same size during a translation

Determine the pre-image shape is congruent to the image Determine the pre-image shape is congruent to the image. Explain your answer 2. Reflection length and angles remain the same size during a translation

Determine the pre-image shape is congruent to the image Determine the pre-image shape is congruent to the image. Explain your answer 3. Rotation The length and angles remain the same size during a translation

Discovering Corresponding part Two geometric figures are congruent if and only if a rigid motion or a composition of rigid motions maps one of the figures onto the other. Because rigid motions preserve length and angle measure A rigid motion maps each part of a figure to a corresponding part of its image. Corresponding parts of congruent figures are congruent. In congruent polygons, this means that the corresponding sides and the corresponding angles are congruent.

Core Concept: CPCT Corresponding parts of congruent figures are congruent. In congruent polygons, this means that the corresponding sides and the corresponding angles are congruent. CPCT: Congruent Part Congruent Triangle

If-then statement for CPCT If the two triangles are congruent THEN their corresponding parts are congruent (the same).

If-then statement for CPCT If their corresponding parts are congruent (the same). THEN the two triangles are congruent

Prove that two triangles are congruent by transformation Given Prove ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹

Prove that two triangles are congruent by transformation Given translate ∆𝐴𝐵𝐶 so that point A maps to point D rotate counterclockwise so that 𝐷𝐶′ coincides with 𝐷𝐹 reflect ∆𝐷 𝐵 ′′ 𝐹 over the line 𝐷𝐹 The reflection maps the sides and angle of ∆𝐷 𝐵 ′′ 𝐹 to the corresponding side and corresponding angle of ∆𝐷𝐸𝐹.

Practice : Prove that two triangles are congruent by transformation Given Prove ∆𝐽𝐾𝐿≅∆𝑇𝑆𝑅

7.3 Can you Get There From Here? Date 2/14/19 Doing Task, Grab your binder Copy down the EQ Work on Warm Up Essential question How can you use transformation to prove that two objects are congurent Warm up: Find the value of x and y

Warm up: Find the value of x and y

Purpose While exploring potential sequences of transformations, students will notice how corresponding parts of congruent figures have to be carried onto one another, and they may look for ways that this can be accomplished in a consistent sequence of steps.

A Develop Understanding Task The two quadrilaterals shown below, quadrilateral ABCD and quadrilateral QRST are congruent, with corresponding congruent parts marked in the diagrams. Describe a sequence of rigid-motion transformations that will carry quadrilateral ABCD onto quadrilateral QRST. Be very specific in describing the sequence and types of transformations you will use so that someone else could perform the same series of transformations.

A Develop Understanding Task The two quadrilaterals shown below, quadrilateral ABCD and quadrilateral QRST are congruent, with corresponding congruent parts marked in the diagrams. Describe a sequence of rigid-motion transformations that will carry quadrilateral ABCD onto quadrilateral QRST. Be very specific in describing the sequence and types of transformations you will use so that someone else could perform the same series of transformations.

Prove that two triangles are congruent by transformation Given Prove Q𝑢𝑎𝑑 𝐴𝐵𝐶𝐷≅𝑄𝑢𝑎𝑑 𝑄𝑅𝑆𝑇

Different Method to the same answer

Quiz/Test Day Date 2/15/19 No notes, you can use your index Card No EQ No Warm Up NO EQ No Warm: Work on your Test/Quiz