Are These Segments Congruent? (Distance Formula)

50 Minute Class, Curriculum, Geometry

Learning Goal: Build procedural fluency with calculating distance between 2 points while maintaining curiosity.

Google Slides


1:1 Lesson

  • Pear Deck
  • Do Ungraded Formative Assessment on paper



  • Common Core
    • HSG.GPE.B.7 – Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
    • HSG.CO.D.12 – Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
  • TEKS
    • G.2(B) – derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines
    • G.5(B) – construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

2 thoughts on “Are These Segments Congruent? (Distance Formula)

  1. Hi Dane!

    I am just thinking out loud and was hoping for some input when you have time.
    One of my biggest challenges with teaching is my pacing. I tend to drag out lessons and I realize that this can create boredom in some students. Then when I try to speed up lessons I feel the stress in the room as I leave some students in the dust.
    Do you ever stop your lessons and then continue them the next day? Or do you skip any undone work and move on to the next lesson, sort of just cutting your losses.
    My other question/thought/concern is this – I am going to implement the ungraded assessments this year. How much time do you leave at the end of class for them? I fear that I’ll do the lesson here, and then not have time for the ungraded assessment at the end of class, leaving students feeling rushed. I am a little embarrassed to post this. I’ve been teaching so long but I still have yet to get a handle on my pacing!
    Thanks for any words of wisdom, advice, ideas. :o) Happy Calculating!

    1. Hey Nicole! No need to be embarrassed! Pacing is something we’re all working on every year, and I think it depends on the class.

      One thing to know about the lessons on this site is that I tend to over plan. I was always afraid of students finishing early, so I tried to plan just a little bit more than what I thought I could get through.

      So, in any lesson, if I know I’m running out of time I try to prioritize problems to finish and just forget about the others. Sometimes I need to get another challenging problem in for the day, so I’ll prioritize that one and forget about some easier ones. Sometimes I really want students to see a spiraled problem to keep improving on old concepts. Either way, having a good idea of the problems you for sure want to get through that day is something to think about.

      If I prioritize and still can’t finish everything I wanted, then saving it for the next day is totally fine. That’s one thing I love about the SBG approach to units. I have quite a few days to work on concepts, so if I need extra time, it’s already built in because I’ve devoted a lot of days on the calendar for concepts. It’s almost like just continuing a story until you finish it.

      As for ungraded assessments, I usually try to allow for the final 10 minutes of class. I want to make sure students have plenty of time to think through it so I can get good work samples. Those assessments are very important to me because I change my next day’s lesson based on the mistakes that arise in the assessment.

      Hope that helps!

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