Module 1 Topic C Lesson 14 Reflections

Transcription

1 Geometry Module 1 Topic C Lesson 14 Reflections The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find line of reflection, get familiar with notations for reflections and express on their own words the properties of reflections Do Now: It is important to review how to contruct the perpendicular bisector of a segment and the perpendicular bisector that goes through an external point. Finding the line of reflection : Instruction steps that are included on the classwork apply for all the lesson Remember the steps for constructing the line of reflection 1. Construct a segment connecting a point on the pre-image and the corresponding point on the image. 2. Construct the perpendicular bisector of that segment Remember the steps for reflecting 1. Construct a line perpendicular to the line of reflection passing through any point on the given shape G-CO.4 G-CO.5 G-CO.12 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 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. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc. Focus Standards

2 Lesson 14 Reflections Warm Up 1. Construct the perpendicular bisector of segment AB 2. Construct the perpendicular bisector of segment CD that goes through an external point A A 3. A rotation is shown below. If the dark P is the preimage and the light P is the image, state the angle of rotation and give the correct notation for this transformation.

3 Lesson 14 Reflections Learning Targets : I can construct the line of reflection using the compass and a straightedge I can draw the reflected figure using a compass and a straightedge I can expres the properties of reflections in my own words Example 1 (Discussion) ABC is reflected across DE and maps onto A B C. Use your compass and straightedge to construct the perpendicular bisector of the segment connecting A to A. What do you notice about the perpendicular bisector? Label the point of intersection of DE and AA ' as point P. What s true about AP and A P? Example 2 a) Using the diagram to the right, construct the line of reflection for quadrilaterals ABCD and A B C D. Label the line of reflection XY. b) If it was known that BC = 5, what is B C? c) If it was known that m ABC = 70 o, find m A B C. d) What type of angle is formed by XY and BB '?

4 In Conclusion So, we just learned that the line of reflection is the of the segment connecting a point on the pre-image and the corresponding point on the image. We also learned that the distance between a point on the pre-image and the line of reflection is to the distance between a point on the image and the line of reflection. In other words, a point on the pre-image and its corresponding point on the image are from the line of reflection. Notation: r l r l (P) = Q Two Basic Properties of Reflections: 1. For any point P on the line l, r l (P) = P. 2. For any point P not on l, r l (P) is the point Q so that l is the perpendicular bisector of the segment PQ. Quick Write Rewrite these two properties in your own words below: Example 3 Construct the line of reflection for the pair of images at right.

5 Reflecting an image over a line of reflection Example 4. Steps to creating the image of a reflection. 1. Construct a line perpendicular to OE passing through A. 2. Using your compass, measure the distance from A to OE along the perpendicular bisector. 3. Using that measurement on your compass, make an arc by putting the tip of your compass on the point of intersection of the perpendicular bisector and OE and drawing an arc that intersects the perpendicular bisector below OE. 4. Label the new point A. 5. Repeat this process for all remaining points.

6 Lesson 14 Reflections Classwork Exercise 1. Construct the line of reflection for the image below. Lesson 14 M1 Remember the steps for constructing the line of reflection 1. Construct a segment connecting a point on the pre-image and the corresponding point on the image. 2. Construct the perpendicular bisector of that segment Exercise 2. Reflect ABCD across line segment EF. Remember the steps for reflecting 1. Construct a line perpendicular to EF passing through any point of the shape

7 For Exercises 3 and 4, construct the line of reflection for each pair of figures. 3) 4) For exercises 5 7, reflect the figure across the line provided. 5) Remember the steps for reflecting Construct a line perpendicular to EF passing through any point of the shape

8 6) 7)