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WSP Incenter-Incircle

  • Incenter-Incircle

    Grade: High School

    This applet allows for the discovery of the incenter and incircle of a triangle.

    Activity

     
    Web Sketchpad Copyright © 2015 KCP Technologies, a McGraw-Hill Education Company. All rights reserved.
    Release: 2015Q2, Semantic Version: 4.2.0, Build Number: 911.6-r, Build Stamp: dn.kcptech.com/20150706050244
    Activity Contents Copyright © 2015 National Council of Teachers of Mathematics. All rights reserved.

    Instructions

    Upon opening the applet, three cities are shown (Helena, Salt Lake, and Boise). These three cities form a triangle.

    How to Use

    You can change the shape of the triangle by dragging any one of the vertices.

    Buttons

    • By clicking on the Find First Angle Bisector button (and any button that pops up afterwards), the next step in the construction will be revealed.
    • At any time, you can press the Reset button to start over.

     

    Exploration

    • What are the properties of the incenter?
       
    • Can an incenter be located outside of the triangle? Why or why not?
       
    • What are the properties of the incircle?
       
    • How would you find the inradius?
      • How about if the triangle were equilateral? 
       
    • Why does this construction work?
      • Prove why the blue circle is indeed the incircle.
       

    Extension

    How many points of concurrency does a triangle have?

    Objectives and Standards

    NCTM Standards and Expectations
    • Geometry / Measurement
    • Functions and Trigonometry
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • High School (9-12)
    • Geometry
    • Measurement