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Constructions

Constructions. Vocabulary. Congruent-the same measurement Construct-to create Straightedge-any object you can use to make a straight line Compass-an instrument used to create circles or parts of circles Arc-part of a circle that can be drawn with a compass. Constructing Line Segments.

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Constructions

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  1. Constructions

  2. Vocabulary • Congruent-the same measurement • Construct-to create • Straightedge-any object you can use to make a straight line • Compass-an instrument used to create circles or parts of circles • Arc-part of a circle that can be drawn with a compass

  3. Constructing Line Segments • Given: A line segment and label it AB A B

  4. Constructing Line Segments • Step 1: Use a straightedge to draw Ray PS so it’s longer than AB A B P S

  5. Constructing Line Segments • Step 2:Place the endpoint in the circle of the safety compass at A and the pencil point on B and tighten down. Draw an arc. A B P S

  6. Constructing Line Segments • 3Keep the same setting on the compass and place the point at P. Draw an arc that intersects PS at a new point Q. A B P Q S

  7. Constructing Congruent Angles • GIVEN: An angle labeled PQR P Q R

  8. Constructing Congruent Angles • 1-Use a straightedge to draw Ray ST P Q R S T

  9. Constructing Congruent Angles • 2- Place the point in the circle of the safety compass at vertex Q. Set your measurement to 2 cm.Draw an arc that intersects both sides of PQR to make points X and Y. X Q Y

  10. Constructing Congruent Angles • 3- Keeping the same setting, place the point at S and draw an arc that intersects ST. Label the intersection Point A. X Q Y S A

  11. Constructing Congruent Angles • 4- Place the compass so that the point is at X and first drawing hole is at Y. Keep that setting and place the point at A. Draw an arc that intersects the arc you drew in Step 3. Label that intersection Point M. X Q Y S A

  12. Constructing Congruent Angles • 5-With the straightedge, draw Ray SM. Angle MST is congruent to Angle PQR.

  13. Bisecting Line Segments • GIVEN a line segment • Step 1- Place the point of the compass at C. Extend the runner until the first drawing hole is more than halfway to D and set it. Draw an arc “above” and “below” CD.

  14. Bisecting Line Segments • 2- Keeping the same setting, place the point on D and draw another arc “above” and another “below” for two new points Q and R.

  15. Bisecting Line Segments • 3- With a straightedge, draw the line segment determined by the two new points. This will intersect the original line. Name the intersection Point M.

  16. What do you think bisect means? • What type of angles are formed by perpendicular segments?

  17. Bisecting Angles • GIVEN- Angle ABC.

  18. Bisecting Angles • Step 1- Place the point of the compass at B and draw an arc that intersects both sides of the angle. Label the points of intersection X and Y.

  19. Bisecting Angles • Step 2- Place the point of the compass at X and move the runner to a length more than halfway to Y. Draw an arc in the interior of Angle ABC.

  20. Bisecting Angles • Step 3- Keep that same setting and place the point at Y and draw an arc that intersects the arc you just drew. Label the intersection T.

  21. Bisecting Angles • Step 4- With a straightedge, draw Ray BT, this is the bisector of Angle ABC.

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