Basic Constructions Constructing Perpendicular Lines

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Presentation transcript:

Basic Constructions Constructing Perpendicular Lines From a point to a line Perpendicular Bisector

Given a line l and a point P not on l, construct a line through P, perpendicular to line l. Step 1: Open your compass so that when you place the point of the compass at P the compass extends past line l, and make an arc that intersects line l in two places. Label these points A and B. P l Put compass point here Put compass point here Put compass point here Step 2: Place the point of your compass at point A and open your compass so that it extends close to B and make an arc below line l. A B C Step 3: Using the same opening, set your compass at B and make an identical arc, so that it intersects the arc you made in step 2. Label this point C.

Given a line l and a point P not on l, construct a line through P, perpendicular to line l. Step 4: Draw P A B l C : The proof of this fact involves the use of congruent triangles.

Given a segment, construct its perpendicular bisector. Step 1: Open your compass so that when you place the point of the compass at A the compass extends more than halfway to B, and make an arc above and below . D Put compass point here Step 2: Using the same opening, place the point of your compass at point B make a similar arc so that it intersects the arc in step 1 twice. Label the two intersection points C and D. A B Put compass point here C Step 3: Draw : The proof of this fact involves the use of congruent triangles. and bisects