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Use the method learned for constructing congruent angles.

Step 1: With the compass point on point H , draw an arc that intersects the sides of H . . Step 3: Put the compass point below point N where the arc intersects HN . Open the compass to the length where the arc intersects line .

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Use the method learned for constructing congruent angles.

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  1. Step 1: With the compass point on point H, draw an arc that intersects the sides of H. Step 3: Put the compass point below point N where the arc intersects HN. Open the compass to the length where the arc intersects line . Keeping the same compass setting, put the compass point above point N where the arc intersects HN. Draw an arc to locate a point. Constructing Parallel and Perpendicular Lines LESSON 3-8 Additional Examples Examine the diagram. Explain how toconstruct 1 congruent to H. Use the method learned for constructing congruent angles. Step 2: With the same compass setting, put the compass point on point N. Draw an arc. Step 4: Use a straightedge to draw line m through the point you located and point N. Quick Check

  2. Step 1: Draw point A and two rays with endpoints at A. Label point B on one ray and point C on the other ray. Step 2: Construct a ray parallel to AC through point B. Constructing Parallel and Perpendicular Lines LESSON 3-8 Additional Examples Construct a quadrilateral with both pairs of sides parallel.

  3. Step 4: Label point D where the ray parallel to AC intersects the ray parallel to AB. Quadrilateral ABDC has both pairs of opposite sides parallel. Constructing Parallel and Perpendicular Lines LESSON 3-8 Additional Examples (continued) Step 3: Construct a ray parallel to AC through point C. Quick Check

  4. With the compass tip on A and B, the same compass setting would make arcs that intersect at point P on line . Without another point, you could not draw a unique line. With the compass tip on A and B, a smaller compass setting would make arcs that do not intersect at all. Once again, without another point, you could not draw a unique line. Constructing Parallel and Perpendicular Lines LESSON 3-8 Additional Examples In constructing a perpendicular to line at point P, why must you open the compass wider to make the second arc? Quick Check

  5. This means that RG intersects line at the midpoint of EF, and RG is the perpendicular bisector of EF. Constructing Parallel and Perpendicular Lines LESSON 3-8 Additional Examples Examine the construction. At what special point does RG meet line ? Point R is the same distance from point E as it is from point F because the arc was made with one compass opening. Point G is the same distance from point E as it is from point F because both arcs were made with the same compass opening. Quick Check

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