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Unit Concept Code Concept Text Video Title 11: Transformations, Congruence, and Similarity G8.I.2 Congruence Determining Whether Triangles Are Congruent Stage Name Date Content writing Content editing Character writing Script review K12 review Revisions Stacey Hannah Melissa Erika ePP 2/3/16 5/2/16 5/5/16 5/7/16 5/24/16 Comments Note that in Row 9, K12 has approved asking a question, pausing, and then explaining without giving answer choices. K12 Signoff Estimated duration: 4:04 CHARACTER INTRODUCTION Voiceover I’m painting constellations on my ceiling! On Screen Developer Instructions 1. Priya is in her bedroom, which should have the same furniture and color palette as in G8C1-3. She is standing on a ladder painting constellations on the ceiling. She holds a brush in one hand and a star-shaped stencil in the other. There is a jar of yellow paint on the shelf on the ladder. The ceiling is a dark blue color. There are two 4’ x 4’ canvas drop cloths overlapping on the floor where she is painting. A light switch should be Sound Effects & References Voiceover On Screen Developer Instructions visible on the wall behind her. Priya has painted a few constellations already— she is in the middle of painting one at the beginning of the scene. She addresses camera. 2. Priya dips her brush in the paint. [Reference for Priya’s position. She may need to be facing the other way on the ladder to be able to access the paint on the shelf as seen in next reference image. She should be more toward the middle of the room rather than right against the wall. The floor (with two 4’ x 4’ canvas drop cloths—one under the ladder and one overlapping it) and the ceiling should both be visible.] Sound Effects & References Voiceover On Screen [Reference for type of ladder Priya should be using. The jar of yellow paint can be on the blue shelf that is on the right side of the ladder in this image.] Developer Instructions Sound Effects & References Voiceover On Screen [Reference for Priya’s progress. These constellations can be arranged in any way that works for the composition of the scene. Do not include the lines connecting the stars – just include the stars themselves. About half of the ceiling should be painted with stars (Priya is halfway through). Developer Instructions Sound Effects & References Voiceover On Screen Do not include the one that has a red x over it—there should be space for one more constellation in addition to the one on which she is currently working. The constellation directly over the ladder should also two or three other stars to represent a constellation in progress. Priya is in the middle of working on this constellation.] [Reference for additional constellations to fill space as needed.] Developer Instructions Sound Effects & References Voiceover On Screen Developer Instructions [Reference for star-shaped stencil. It should appear to be made of thin plastic. There should be one complete star in the stencil—no partial pieces as seen at the bottom of the reference. The star-shaped space in the stencil should be the same size as the stars painted on the ceiling. The stars should be relatively small but still visible on the ceiling.] 2 I’m using a stencil to make sure that all of the stars are exactly the same shape and size. See? 1. Shot changes to closeup of area on ceiling above Priya where where two of the lines in the constellation she is painting meet. As she works, she looks at what she is doing. 2. Priya holds the stencil against the ceiling where the two lines meet. [Reference for approximate shot. Priya’s 3. Priya uses the brush to paint in the Sound Effects & References Voiceover 3 We can use angle measures and side lengths to help determine whether two polygons have the same shape and size. Let’s check it out! On Screen Developer Instructions other hand should be visible holding the star-shaped stencil. Other stars she has already painted should also be visible.] star-shaped stencil. 4. Priya lifts the stencil away, revealing a yellow star shape on the ceiling the same size as the stencil. 1. Shot changes to that in Row 1, with Priya on ladder holding the brush and stencil and addressing camera. Sound Effects & References WHITEBOARD MATH ANIMATION 4 Voiceover On Screen Developer instructions We’re asked to determine which triangles are congruent. Which triangles are congruent? 1) Which triangles are congruent? // Also show the art: sides AB, KL, and ST measure 5 units, sides BC and RT measure 3 units, sides AC and RS measure 5.83 units, side LM measures 2.2 units, and side KM measures 5.46 units. Angles B, L, and T are right angles. Label and mark as shown. Congruent polygons have exactly the same size and shape. 2) Congruent Polygons: Have the same size and shape // “Congruent Polygons” is a heading. Congruent polygons: Have the same size and shape 5 The corresponding parts of two polygons are the parts that match up with each other. Which triangles are congruent? 3) // Make “same size” in the last line blue. 4) // Make “shape” in the last line blue. 1) Congruent Polygons // Heading. 2) • All pairs of corresponding sides are congruent. // Make “All pairs” and “corresponding sides” blue. When two polygons are congruent, all pairs of corresponding sides and all pairs of corresponding angles are congruent. 3) • All pairs of corresponding angles are congruent. // In this text, make “All pairs” and “corresponding angles” orange. Congruent Polygons Sound Effects & References Voiceover On Screen Developer instructions All pairs of corresponding sides are congruent. 6 Let’s start by comparing the first and second triangles. All pairs of corresponding angles are congruent. Which triangles are congruent? Sides marked with the same number of tick marks are congruent. So, sides ‘A B’ and ‘K L’ are congruent. The other pairs of corresponding sides do not have the same number of tick marks, so we only know for sure that one pair of corresponding sides is congruent. Angles marked with the same number of tick marks are congruent. Right angles are also congruent. So, angles B and L are congruent because they are both right angles. The other pairs of corresponding angles are not right angles and do not have the same number of tick 1) First and Second Triangles // Heading. 2) // Make triangles ABC and KLM and their labels and markings blue. 3) // Change all to black. In the art, make sides AB and KL and the tick marks on these sides blue. First and Second Triangles 4) • Only one pair of corresponding sides is congruent. // Make “one pair” and “corresponding sides” blue. Only one pair of corresponding sides is congruent. 5) // Change the art to black. Only one pair corresponding angles is congruent. The triangles are not congruent. 6) // In the art, make the sides forming angles B and L blue; make the right angle symbols for these angles orange. 7) • Only one pair corresponding angles is congruent. // In this text, make “one pair” and “corresponding angles” orange. 8) • The triangles are not congruent. // In the art, change all to black. Make the Sound Effects & References Voiceover On Screen marks, so we only know for sure that one pair of corresponding angles is congruent. 7 So the first and second triangles are not congruent. Next, let’s compare the first and third triangles. Developer instructions tick marks on sides AB and KL blue. Make the right angle symbols for angles B and L orange. Change all text to black. Make “not congruent” blue. Which triangles are congruent? [Change all back to black.] 1) First and Third Triangles // Heading. Sides ‘B C’ and ‘T R’ both have one tick mark. Sides ‘A B’ and ‘S T’ both have two tick marks. And sides ‘A C’ and ‘S R’ both have three tick marks. 2) // Make triangles ABC and TSR and their labels and markings blue. 3) // Change all to black. In the art, make sides BC and TR and the tick marks on these sides blue. (Don’t make the endpoints or labels blue.) So, all pairs of corresponding sides are congruent. Angles A and S both have one tick mark. Angles C and R both have two tick marks. And angles B and T are both right angles. All pairs of corresponding angles are congruent. So, the first and third triangles are congruent. First and Third Triangles All pairs of corresponding sides are congruent. All pairs corresponding angles are congruent. The triangles are congruent. 4) // In the art, make sides AB and ST and the tick marks on these sides orange. (Don’t make the endpoints or labels orange.) 5) // In the art, make sides AC and SR and the tick marks on these sides purple. (Don’t make the endpoints or labels purple.) 6) • All pairs of corresponding sides are congruent. // Make “All pairs” and Sound Effects & References Voiceover On Screen Developer instructions “corresponding sides” blue. 7) // Change the art to black. Then change the sides of angles A and S to blue and make the tick marks in these angles blue. 8) // In the art, change the sides of angles A and S to black (but keep the tick marks blue). Change the sides of angles C and R to orange and make the tick marks in these angles orange. 9) // In the art, change the sides of angles C and R to black (but keep the tick marks orange). Change the sides of angles B and T to purple and make the right angle symbols in these angles purple. 10) • All pairs corresponding angles are congruent. // In the art, change the sides of angles B and T to black (but keep the right angle symbols purple). Make “all pairs” and “corresponding angles” in this text blue. 11) • The triangles are congruent. // In the art, make the tick marks on sides BC and RT blue, make the tick marks on sides AB and ST orange, and make the tick marks on sides AC and SR purple. Sound Effects & References Voiceover 8 Because the first and third triangles are congruent, we can write a congruence statement. Start by naming the first triangle ‘A B C.’ Then write the congruence symbol. Next, name the other triangle by listing corresponding vertices in order. S corresponds to A. T corresponds to B. And R corresponds to C. Triangle ‘A B C’ is congruent to triangle ‘S T R.’ On Screen Developer instructions Which triangles are congruent? Change all text to black. Make “congruent” in this text blue. [Change all back to black] 1) // In the art, make the tick marks on sides BC and RT blue, make the tick marks on sides AB and ST orange, and make the tick marks on sides AC and SR purple. Make the tick marks in angles A and S blue, make the tick marks in angles C and R orange, and make the right angle symbols in angles B and T purple. First and Third Triangles △ ABC @ △STR △ 2) ABC // Make blue. Animate the appearance of the letters by cloning them in the first triangle and moving them down. 3) @ // Change “ Make “ @ ” blue. △ ABC ” back to black. △ 4) S // Change “ @ ” back to black. In the art, make the labels “A” and “S” blue. In the last line of text, make “A” and “S” blue. Animate the appearance of the letter by cloning it in the third triangle and moving it down. 5) T // In the art, make the labels “B” and “T” purple. In the last line of text, make Sound Effects & References Voiceover On Screen Developer instructions “B” and “T” purple. Animate the appearance of the letter by cloning it in the third triangle and moving it down. 9 Do think the second and third triangles are congruent? Which triangles are congruent? 6) R // In the art, make the labels “C” and “R” orange. In the last line of text, make “C” and “R” orange. Animate the appearance of the letter by cloning it in the third triangle and moving it down. [Change all back to black.] 1) Are the second and third triangles congruent? // Make triangles KLM and TSR and their labels and markings blue. 2) // Pause 2 seconds. 10 The second and third triangles are not congruent. We know the first and third triangles are congruent, and we know that the second triangle is not congruent to the first triangle. That means the second and third triangles are not congruent either. Of the three triangles, only triangles ‘A B C’ and ‘S T R’ are congruent. Which triangles are congruent? [Change all back to black] △ △ 1) Only ABC and STR are congruent. // In the art, make triangles ABC and TSR and their labels and markings blue. Make “ ABC ” and △ “ STR ” blue. Only △ ABC and △STR are congruent. △ Sound Effects & References CHARACTER CONCLUSION Voiceover 11 On Screen We determined which of three triangles are congruent. Developer instructions 1. The scene is as it was in Row 1, with the ladder set up, but Priya is standing on the floor with her hand on the light switch. The constellation she was painting is complete. I’m going to enjoy my new constellations! 2. Priya flips the light switch. The room dims and the stars glow bright on the ceiling. Priya looks up at the ceiling. [Reference for darkness of room and bright yellow glow of stars on the ceiling. The pattern of stars should be the same as that in Row 1, with the constellation Priya was working on completed.] Sound Effects & References