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12 Aug 9:50 - 11:20 Geometry Go over Part 2 of Introductory Activity Collect Signature page-Pick up Textbook Check Vocabulary - how useful was your reference? Practice Exercises Transformational Geometry - Translations 2. Brian is correct. Every square is also a rectangle. A rectangle is defined as a quadrilateral with four right angles and since a square is a quadrilateral which has four right angles it can also be called a rectangle. Brian made a convincing argument because he clearly explained how the familiar definition of a rectangle also applies to a square. 2. Brian is correct. Every square is also a rectangle. A rectangle is defined as a quadrilateral with four right angles and since a square is a quadrilateral which has four right angles it can also be called a rectangle. Brian made a convincing argument because he clearly explained how the familiar definition of a rectangle also applies to a square. Is every rectangle also a square? 3. Consider the following set of figures on a coordinate plane. a. Which of the following figures are parallelograms? How do you know? A parallelogram is a quadrilateral (4 sides) both pairs of opposite sides are parallel and same length (congruent); diagonals bisect. Parallel sides will have same slope. Check our definition in Part 1. 3. Consider the following set of figures on a coordinate plane. a. Which of the following figures are parallelograms? How do you know? ABCD, EFGH, IJKL, MNOP, and QRST are all parallelograms. I know because they all have two pairs of parallel sides which is the definition of a parallelogram. I can tell the sides are parallel when they have the same slope (rise/run). 3. Consider the following set of figures on a coordinate plane. a. Which of the following figures are parallelograms? How do you know? UVWX is not a parallelogram because the slope of UX is 3 and the slope of VW is 4, so these sides are not parallel. (Parallel lines remember have the same slope) 3.b. Can you identify all of the parallelograms? Write an argument that would convince a skeptic that you have found all of the parallelograms in this figure. ABCD is a parallelogram because the slope of AD is the same as the slope of BC (no slope, 0, horizontal line segments). The slope of AB is the same as the slope of DC (slope = 3/2). Hence ABCD is a quadrilateral with both pairs of opposite sides that are parallel, a parallelogram. 3.c. Could you classify any of the parallelograms as another type of mathematical shape? If so, which ones? If not, why not? 3.c. Could you classify any of the parallelograms as another type of mathematical shape? If so, which ones? If not, why not? IJKL is a square because the slope of IJ=slope of KL = -2 and the slope of JK = slope of IL= ½ . -2 and ½ are opposite reciprocals , so KL is perpendicular to JK, which means they are at right angles (90°). 3.c. Could you classify any of the parallelograms as another type of mathematical shape? If so, which ones? If not, why not? QRST is a rectangle MNOP is a rhombus UVWZ is a kite 4. Martin said “Quadrilateral ABCD is a rhombus because AB||DC and AD||BC and it doesn’t have any right angles.” || parallel Simone said: “Quadrilateral ABCD is a rhombus because it has two pairs of parallel sides and AB=BC=CD=DA.” 4. Martin said “Quadrilateral ABCD is a rhombus because AB||DC and AD||BC and it doesn’t have any right angles.” (the fact that there aren’t any right angles is not relevant to the argument that this shape is a rhombus. A square does have right angles, and it is also a rhombus. Simone said: “Quadrilateral ABCD is a rhombus because it has two pairs of parallel sides and 4. Simone said: “Quadrilateral ABCD is a rhombus because it has two pairs of parallel sides and AB=BC=CD=DA.” This is the better argument since it mentions that a rhombus has 2 pairs of parallel sides and also that all 4 sides are congruent. 4. Simone said: “Quadrilateral ABCD is a rhombus because it has two pairs of parallel sides and AB=BC=CD=DA.” A more precise mathematical argument might include naming the parallel sides. AB||DC and AD||BC. (Could also state the slopes of the parallel sides(3 and ⅓) Bring up signature page and sign for textbook. Find vocabulary in textbook, add page reference and make sure what you have matches what the textbook says (reliable source). Continue to complete the table. Practice Exercises. Draw a picture that represents what is described in the following problems. 1) Plot a point, C, on rayAB so that AC<AB. (Distance from A to C is less than distance from A to B.) Practice Exercises. Draw a picture that represents what is described in the following problems. 2) Draw line segment DE so that it intersects (crosses) line FG at H, and so that angle DHF is obtuse (greater than 90 degrees). Practice Exercises. Draw a picture that represents what is described in the following problems. 3) Draw two supplementary angles, angle IJK and angle LJK (measure of the two angles adds up to 180 degrees). What type of angle is angle IJL? Practice Exercises. Draw a picture that represents what is described in the following problems. 3) Draw two supplementary angles, angle IJK and angle LJK (measure of the two angles adds up to 180 degrees). What type of angle is angle IJL? A straight angle. Practice Exercises. Draw a picture that represents what is described in the following problems. 4) Draw a triangle MNP so that angle MNP is a right angle. Angle NPM and angle PMN are _______ angles. Practice Exercises. Draw a picture that represents what is described in the following problems. 4) Draw a triangle MNP so that angle MNP is a right angle. Angle NPM and angle PMN are acute angles. Practice Exercises. Draw a picture that represents what is described in the following problems. 5) Draw line p, line q, line r and line s so that p is parallel to q, r is parallel to s and p is perpendicular to r. What type of quadrilateral appears to be formed by your lines? Practice Exercises. Draw a picture that represents what is described in the following problems. 5) Draw line p, line q, line r and line s so that p is parallel to q, r is parallel to s and p is perpendicular to r. What type of quadrilateral appears to be formed by your lines? rectangle Practice Exercises. Draw a picture that represents what is described in the following problems. 6) Draw triangle TUV so that it shares a side with quadrilateral UVWX. Practice Exercises. Describe 3 characteristics that appear to be true in the drawing. Use appropriate notation and vocabulary. Transformational Geometry Translations A transformation is a change in the position, size, or shape of a figure. A translation is a transformation which moves each point of a figure the same distance and in the same direction. Example 1. △ABC is translated 1 unit right and 4 units up. Draw the image △A’B’C’. This would be represented by T1,4 Example 1. What are the coordinates of A (1, -3) A’ B (3, 0) B’ C (4, -2) C’ Example 1. What are the coordinates of A (1, -3) A’ (2, 1) B (3, 0) B’ (4, 4) C (4, -2) C’ (5, 2) Example 2. Example 2. T-4, 5 What are the coordinates of: J (0, 2) J’ (-4, 7) K (3, 4) K’ (-1, 9) L (5, 1) L’ (1, 6)