Lesson Context Lesson Objectives: Warm-up: S(10,-3) T(-7,-5)
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1 Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: mastery with algebraic skills to be used in our work with co-ordinate geometry (midpoint, length, slope) understanding various geometric properties of quadrilaterals & triangles how do you really prove that something is true? Where we ve been Where we are Where we are heading You know how to find a midpoint, a length & slope and how to work with GeoGebra Using length, slope & midpoint in classifying geometric figures How can I prove various geometric properties of quadrilaterals and triangles? Lesson Objectives: a. Review the properties of quadrilaterals through GeoGebra b. Use algebraic methods to classify triangles Warm-up: Distance/Length: d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 Slope: m = y y 2 1 x 2 x 1 Midpoint: x 1 + x 2 2, y 1 + y 2 2 Given the two points S(10,-3) and T(-7,-5). Find the: a. distance b. slope c. midpoint
2 A: Exploring Quadrilaterals through dynamic geometry software: GeoGebra Quadrilateral Type: Use these points to construct each shape on GeoGebra: Properties: DESCRIBE how you would confirm each property ALGEBRAICALLY: Square A(-1, -2) B(5, 2) C(1, 8) D(-5,4) Rhombus A(-4, 4) B(1, 6) C(-1, 1) D(-6, -1) Rectangle A(-6, 1) B(-3, -2) C(2, 3) D(-1,6) Parallelogram A(-3, 2) B(4, 4) C(2, -1) D(-5, -3) Trapezoid A(-3, 4) B(3, 2) C(2, -1) D(-5, -2) Quadrilateral A(-3, 5) B(2, 2) C(4, -3) D(-5, -1)
3 B: Quadrilateral Flow Chart:
4 C: Classifying Quadrilaterals given slopes and lengths of each side: 1. Classify quadrilateral BEAR, where: Slope of BE = 1 3 Slope of EA = 3 Slope of AR = 1 3 Slope of BR = 3 Length of BE = 10 Length of EA = 10 Length of AR = 10 Length of BR = 10 BEAR is a. 2. Classify quadrilateral OHMY, where: Slope of OH = 1 3 Slope of HM = 3 Slope of MY = 1 3 Slope of OY = 3 Length of OH = 10 Length of HM = 2 10 Length of MY = 10 Length of OY = 2 10 OHMY is a. 3. Classify quadrilateral WZRD, where: Slope of WZ = 0 Slope of ZR = 4 3 Slope of RD = 0 Slope of WD = 4 3 Length of WZ = 5 Length of ZR = 5 Length of RD = 5 Length of WD = 5 WZRD is a. 4. Classify quadrilateral AHSZ, where: Slope of AH = 1 4 Slope of SZ = 6 7 Slope of HS = 4 Length of AH = 17 Length of SZ = 85 Length of HS = 17 Length of ZA = 85 AHSZ is a. Slope of ZA = 9 2
5 D: Classifying Quadrilaterals in the coordinate plane: Classify quadrilateral ABCD with vertices at A(4,7), B(9,7), C(6,3), D(1,3). Step 1: Plot the points in the coordinate plane. Step 2: Use the distance formula to find the length of each side: AB = BC = CD = DA = Step 3: Check for parallel lines and right angles by checking the slopes of each side. The slope of AB = Step 4: Classify ABCD. Therefore ABCD is a. The slope of BC = The slope of CD = The slope of DA =
6 E: Classifying Quadrilaterals in the coordinate plane: Classify quadrilateral ABCD with vertices at A(-2,5), B(1,8), C(4,5), D(1,2). Step 1: Plot the points in the coordinate plane. Step 2: Use the distance formula to find the length of each side: AB = BC = CD = DA = Step 3: Check for parallel lines and right angles by checking the slopes of each side. The slope of AB = Step 4: Classify ABCD. Therefore ABCD is a. The slope of BC = The slope of CD = The slope of DA =
7 F: Classifying Quadrilaterals in the coordinate plane: Classify quadrilateral ABCD with vertices at A(3,6), B(9,-2), C(5,-8), D(-5,-6). Step 1: Plot the points in the coordinate plane. Step 2: Use the distance formula to find the length of each side: AB = BC = CD = DA = Step 3: Check for parallel lines and right angles by checking the slopes of each side. The slope of AB = Step 4: Classify ABCD. Therefore ABCD is a. The slope of BC = The slope of CD = The slope of DA =
8 G: Classifying Quadrilaterals in the coordinate plane: Classify quadrilateral ABCD with vertices at A(-5,4), B(5,4), C(5,-5), D(-5,-5). Step 1: Plot the points in the coordinate plane. Step 2: Use the distance formula to find the length of each side: AB = BC = CD = DA = Step 3: Check for parallel lines and right angles by checking the slopes of each side. The slope of AB = Step 4: Classify ABCD. Therefore ABCD is a. The slope of BC = The slope of CD = The slope of DA =
9 H: Classifying Quadrilaterals in the coordinate plane: Graph quadrilateral ABCD which has coordinates: A(-2,-3) B(0,4) C(6,4) D(4,-3) Classify quadrilateral ABCD.
10 I: Classifying Quadrilaterals in the coordinate plane: Graph quadrilateral ABCD which has coordinates A(-5,3) B(-1,5) C(1,-4) D(-3,-5) Classify quadrilateral ABCD.
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