Urban Oasis SlidesUrban Planning Division URBAN OASIS Finding the Heart of the City PROJECT ID: INC-2026 The Dilemma "Our city needs a new green space. To make it fair for all commuters, the park must be the exact same walking distance from all three major highways." Highways form a large triangle in the city center. "Distance" means the shortest path to the road (perpendicular). Where do we put it? The Geometry Solution Training Video Embedded media Focus on the relationship between bisectors and side distance (1:54 - 2:53) Look For: What lines meet? What distance is equal? The "Inscribed Circle" Blueprint Basics Angle Bisectors When we cut all three corners of the highway triangle in half, they meet at one single point. The Incenter This point is the equidistant hub. Its distance to any highway is measured at a 90° angle. Design Challenge STEP 1 Use your protractor to find and mark the angle bisectors for each highway intersection. STEP 2 Mark the Incenter as "Park Location P" where the lines meet. STEP 3 Measure the distance to the roads using your ruler and convert using the 1:100 scale. Time Remaining: 25 Minutes Ruler Protractor Map
Highway Hub Map HandoutUrban Oasis: Highway Hub Map Department of Urban Planning & Design NAME: DATE: MISSION BRIEFING Your task is to locate the optimal site for the Central Park Project. The park must be exactly the same walking distance from the center-lines of Route 101, Highway 5, and Interstate 80. Use your tools to construct the incenter on the map below. SCALE: 1 inch = 100 meters Route 101 Highway 5 Interstate 80 1. Angle Bisector Construction Use your protractor to bisect the three angles formed by the highways. Draw the bisectors clearly. 2. Point of Concurrency Label the point where all three bisectors meet as Park Location P. Found it! Planning Calculations Measured distance from Park P to nearest road (inches): Calculated real-world distance (meters): Use the scale 1 in = 100 m Check your work: Is the distance to Highway 5 the same as the distance to Interstate 80? Yes No Map Reference: GRID-INC-B Authorized for Classroom Use Only
Geometry Tool Kit HandoutGeometry Tool Kit Standard Issue Urban Planning Equipment FIELD ASSEMBLY INSTRUCTIONS 1. Carefully cut out the ruler and protractor along the dashed lines. 2. For best results, glue these to a piece of cardstock or thin cardboard before cutting. 3. Use the protractor to find the exact middle (bisector) of each highway intersection angle. 4. Use the ruler to measure the perpendicular distance from the incenter to the roads. 6-Inch Planning Ruler (1:1 Scale) 0 1 2 3 4 5 6 180-Degree Angle Bisector Tool 0 90 180 180° 90° 0° PRINT AT 100% SCALE FOR ACCURATE MEASUREMENTS
Reflection Journal PromptsField Notes: Project Incenter Planning & Logistics Department DOCUMENT REF: REF-2026-004 Lead Planner: Date: 1 Why was the Incenter the correct choice for this park placement instead of the Centroid? Consider the difference between "equidistant from vertices" (circumcenter), "balance point" (centroid), and "equidistant from sides" (incenter). 2 Imagine you are designing a high-security vault inside a triangular building. Why would the incenter be the most secure location? 3 Technical Challenge: Which part of the construction process required the most precision? How did your tools (protractor/ruler) help or hinder your accuracy? Completed Verified Filed
Teacher Facilitation GuideTeacher Facilitation Guide Lesson: The Perfect Park (Incenter) Subject: Geometry Grades: 9-10 LESSON FLOW 05 MIN Hook: Present the "Urban Oasis" scenario. Ask students: "If you're between three roads, where is the fairest spot for everyone?" 10 MIN Direct Instruction: Watch video (1:54-2:53). Teacher Tip: Pause at 2:28 to discuss why "distance to a line" must be perpendicular. 25 MIN Design Challenge: Students use the Highway Hub Map and Tool Kit to construct the incenter and calculate real-world distances. 05 MIN Reflection: Students complete the Field Notes journal prompts to solidify the conceptual difference between concurrency points. Key Concepts Incenter: Intersection of angle bisectors. Equidistant: Same distance from all 3 sides. Shortest Path: Perpendicular distance. Answer Key: Highway Hub Map CONSTRUCTION CHECKLIST Angle Bisectors: All three lines should meet at a single point (P). If they form a small "error triangle," have students re-measure their angles. Park Location P: Should be roughly centered within the map's highway triangle. Distance P to Side: Using the provided map scale, the perpendicular distance from P to any road should be approximately 1.25 to 1.35 inches. CALCULATION SOLUTIONS MEASURED DISTANCE ~ 1.3 inches REAL-WORLD CALCULATION (1:100) 1.3 in × 100 m/in = 130 meters COMMON MISCONCEPTION Students often confuse the Incenter with the Circumcenter. Remind them: Incenter = Same distance to SIDES (Park to Road). Circumcenter = Same distance to VERTICES (Park to Intersections). DIFFERENTIATION Scaffold: Provide a partially completed map with one bisector already drawn. Extension: Ask students to draw the "Incircle" using a compass to see if it perfectly touches all three highways.
