10-2 Perpendicular and Parallels

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Presentation transcript:

10-2 Perpendicular and Parallels (Euclidean) Constructing a perpendicular bisector. 1) Point on one end, arc up and down. 2) Switch ends and do the same 3) Draw line through intersection All radius same, rhombus, diagonals bisect each other. This is DIFFERENT from book (slightly). Make sure when you get help, they understand the method we are using in class at times.

(Euclidean) Constructing a perpendicular to a line through a given point on the line. 1) From the given point, pick any arc and mark the circle left and right. 2) Those two marks are your endpoints, and construct a perpendicular bisector just like the previous slide. Justification. Line is perpendicular by construction, 3 is on the bisector because it is equidistant to both endpoints (because radii are equal), so the line is going through the point.

(Euclidean) Given a point off a line, draw a line perpendicular to line from given point. 1) From the given point, pick any arc and mark the circle left and right. 1) Put your left foot in, then put your left foot out. 2) Those two marks are your endpoints, and construct a perpendicular bisector just like the previous slide. Justification. Line is perpendicular by construction Drawing the perpendicular is crucial, this is eventually used for altitude, midpoint, median, and obviously perpendicular bisector. (Let’s discuss how)

(Modern) Given a line and a point, construct a line parallel to the given line through the given point. 1) Pick any point on the line, draw a line from there through the given point. 2) Using the angle formed by the given line and the drawn line, make a congruent angle using the given point as the vertex. Justification: Converse of corresponding angles theorem. Similar to the concept from your homework last night, C level problem 25.

Let’s make a square given a side length (make your own on your paper, no, it doesn’t have to be the same size as mine, it doesn’t matter. There are many ways to do this, try your own method and see what is most efficient, your way could be better than Mr. Kim’s!

HW #19: Pg 382: CE 2-5; Pg 383: 5-8, 14-16, 18, 20, 22, 24, 25, 27