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Lesson Plan #2 Class: Wahlert Catholic High School, 4th period Grade Level: Geometry (Freshman and Sophomores) 90 mins. Unit: 6.5 – Trapezoids and Kites Teacher: Mrs. Nicole Sisler Common Core State Standards (CCSS) Algebra o Seeing Structure in Expressions Write expressions in equivalent forms to solve problems (midsegment) o Reasoning with Equations and Inequalities Solve equations and inequalities in one variable Geometry o Congruence Prove geometric theorems Make geometric constructions o Similarity, Right Triangles, and Trigonometry Define trigonometric ratios and solve problems involving right triangles 21st Century Skill(s) Creativity and Innovation Collaboration Problem Solving Objectives By the end of class today, students will be able to identify the bases and legs of a trapezoid. By the end of class today, students will be able to recognize if a trapezoid is isosceles. By the end of class today, students will be able to compute the midsegment of a trapezoid (based on Theorem 6.17). By the end of class today, students will be able to determine the lengths of the sides of the kite when given the measure of the diagonals. By the end of class today, students will be able to calculate the measure of the interior angles of a trapezoid and a kite. Anticipatory Set [5 minutes] Show first slide of presentation. Ask students what these shapes are called (trapezoids and kites). Ask students what properties they think these quadrilaterals have (based on properties discussed in the last couple days’ classes of polygons and quadrilaterals). Teaching: Activities [80 minutes] Trapezoids [35 minutes] DEFINE: Trapezoid – a quadrilateral with exactly one pair of parallel sides o Bases – Parallel sides: AB and DC o Base angles: D and C; A and B o Legs – Nonparallel sides: DA and BC Leg angles are supplementary (added together to equal 180): A and D, B and C (draw on board) – NOT base angles A and B, D and C o Isosceles trapezoid – legs are congruent (equal) THEOREMS: (book) Examples (Powerpoint) o Isosceles trapezoids – Congruent sides o Irregular trapezoids – Supplementary angles DEFINE: Midsegment – segment that connects the midpoints of its legs o THEOREM: (Book) o Easy way to remember this is you’re finding the average/middle. If I asked you to find the average of 3 and 9, what would it be? (6) How did you get this? (3+9=12, 12 / 2 values = 6) It’s the same thing here – you add both bases (parallel sides), and divide by the number of bases (2). Examples (Homework) o Midsegment 6.5 A #13 on homework – 7+13 = 20 / 2 = 10 Change numbers: Longer base = 15, Midsegment = 10. What is measure of shorter base? (5) Exploration (Powerpoint) [15 minutes] o Website: http://www.mathsisfun.com/geometry/trapezoid.html Reminder of appropriate laptop use at this time. No other websites or Skype. If students can’t stay focused they’ll have to make trapezoids without use of laptop. Show this! - Have students go to website with a partner. Scroll 1/3 of the way down to the portion of the website where you can experiment with the trapezoid. Students are to spend a minute or two playing with it to make different trapezoids. Then have each set of partners record two trapezoids – one isosceles and one not (and denote which is which). For the isosceles trapezoid, have students include measure of only one angle. For non-isosceles trapezoids, have students include measure of two angles and both base lengths. Then have students swap papers with another group. Students find all remaining angles on both trapezoids as well as the length of the midsegment on the non-isosceles trapezoid. This will be submitted as an exit slip to assess objectives – not for a grade. Kites [30 minutes] DEFINE: Kite – quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. o What does this really mean? Two sets of adjacent (right next to each other) sides are congruent (the same) THEOREM: (Book) Short diagonal is bisected – it’s split in half (NOT true for the long diagonal!) Examples (Last example – homework) o Diagonals o Angles What theorem or formula do we know that would come in handy if we know the lengths of the diagonals? Hint: The diagonals split the kite into 4 triangles. (Pythagorean Theorem) XY = YZ = 16.97 WX = WZ = 23.32 What is the measure of angle J? (84) – Theorem 6.19 (one pair of opposite congruent angles) What is the measure of angle G? (84) o 6.5 A #18 homework – Angle E = 118, Angle K = 50 o Assessment - Thumbs up if it’s making sense, thumbs down if you’re completely lost, in between if you’re in between Closure [5 minutes] We’ve examined properties and theorems of trapezoids and kites today. What are some of the properties? (Write on board) o Trapezoids: If isosceles trapezoid then base angles are congruent If base angles are congruent then it’s an isosceles trapezoid Isosceles trapezoid if and only if diagonals are congruent Leg angles are supplementary (add to 180) Midsegment is sum of bases divided by 2 o Kites: Diagonals are perpendicular Exactly one pair of opposite angles congruent Two pairs of consecutive congruent sides (but opposite sides are not congruent) Can use Pythagorean Theorem with diagonals to find segment lengths This will continue to be important as we continue our understanding of quadrilaterals and their properties. Are there any other questions from the concepts we looked at today? Turn in exit slip from exploration piece. Assessment By the end of class today, students will be able to identify the bases and legs of a trapezoid. o This objective will be assessed by judgment of class participation and responses. By the end of class today, students will be able to recognize if a trapezoid is isosceles. o This objective will be assessed by the exploration website piece that is submitted by students at the end of class. By the end of class today, students will be able to compute the midsegment of a trapezoid (based on Theorem 6.17). o This objective will be assessed by the exploration website piece that is submitted by students at the end of class. By the end of class today, students will be able to determine the lengths of the sides of the kite when given the measure of the diagonals. o This objective will be assessed by thumbs up/thumbs down. By the end of class today, students will be able to calculate the measure of the interior angles of a trapezoid and a kite. o This objective will be assessed by the exploration website piece that is submitted by students at the end of class as well as by thumbs up/thumbs down.