Warm up IMAGE- new On desk 5.7 figure (5 min) Types of transformations: -rotation, reflection, translation(moves), and dilation(enlargement or reduction)

Do Daily Quiz Tangrams Hands-on/Paper Cut-out

5.7 ESSENTIAL QUESTION How do you identify reflections and lines of symmetry?

VOCABULARY A reflection is a transformation that creates a mirror image.

Properties of Reflections 1. The reflected image is congruent to the original figure. (size & shape)

Properties of Reflections 1. The reflected image is congruent to the original figure. 2. The orientation of the reflected image is reversed (inverted)

Properties of Reflections 1. The reflected image is congruent to the original figure 2. The orientation of the reflected image is reversed 3. The line of reflection is the perpendicular bisector of the segments joining the corresponding points/objects (symmetry).

Properties of Reflections 1. The reflected image is congruent to the original figure (size & shape) 2. The orientation of the reflected image is reversed (inverted) 3. The line of reflection is the perpendicular bisector of the segments joining the corresponding points/objects (symmetry).

Check three properties: Example 1 Identify Reflections Tell whether the red triangle is the reflection of the blue triangle in line m. SOLUTION Check three properties: 1. Is the image congruent to the original figure? Yes. 2. Is the orientation of the image reversed? Yes. 3. Is m the perpendicular bisector of the segments connecting the corresponding points? Yes. Cont. 9

Example 1 Identify Reflections Continuation.... Because all three properties are met, the red triangle is a reflection of the blue triangle in line m. ANSWER 10

Check to see if all three properties of a reflection are met. SOLUTION Example 2 Identify Reflections Tell whether the red triangle is the reflection of the blue triangle in line m. Check to see if all three properties of a reflection are met. SOLUTION 1. Is the image congruent to the original figure? Yes. 2. Is the orientation of the image reversed? No. The red triangle is not a reflection of the blue triangle. ANSWER 11

Which segment is the reflection of AB in the x-axis? Which point Example 3 “Reflections in a Coordinate Plane” Which segment is the reflection of AB in the x-axis? Which point corresponds to A? to B? a. b. Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B? SOLUTION a. The x-axis is the perpendicular bisector of AJ and BK, so the reflection of AB in the x-axis is JK. A(–4, 1) J(–4, –1) B(–1, 3) K(–1, –3) 12

Example 3 Reflections in a Coordinate Plane Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B? b. The y-axis is the perpendicular bisector of AD and BE, so the reflection of AB in the y-axis is DE. A(–4, 1) D(4, 1) B(–1, 3) E(1, 3) 13

Checkpoint Identify Reflections Tell whether the red figure is a reflection of the blue figure. If the red figure is a reflection, name the line of reflection. 1. 2. 3. ANSWER yes; the x-axis ANSWER no ANSWER yes; the y-axis

Determine the number of lines of symmetry in a square. Example 4 Determine Lines of Symmetry Determine the number of lines of symmetry in a square. SOLUTION Think about how many different ways you can fold a square so that the edges of the figure match up perfectly. vertical fold horizontal fold diagonal fold diagonal fold ANSWER A square has four lines of symmetry. 15

Determine the number of lines of symmetry in the figure. Checkpoint Determine Lines of Symmetry Determine the number of lines of symmetry in the figure. 1. ANSWER 1 2. ANSWER 2 3. ANSWER 4

Review

Find the value of x. 2. 1. ANSWER x = 3 3. Find RS. ANSWER x = 7 ANSWER RS = 8

DE bisects A of equilateral triangle ABC DE bisects A of equilateral triangle ABC. Explain why DE is a perpendicular bisector of BC. 4. ANSWER Because the triangle is equilateral, the angle bisector of A divides ∆ABC into two congruent right triangles. Thus, DE BC and the point of intersection is equidistant from B and C. 

Hw 5.7A