unit 4 guided notes - northshore school district ?· constructions with perpendicular and parallel...

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  • Unit 4 Guided Notes Name ________________________ Geometry Per ______ Date _______________ The allowed construction tools are _______________, _________________, and ___________________.

    NEVER use a ____________________ to measure an angle during a construction. NEVER use a

    _________________ to measure a segment length during a construction.

    Instructions:

    I. Complete all constructions on this piece of paper. Some constructions will require you to use the reference objects given below.

    II. Write detailed numbered instructions for how you completed.

    Reference Objects: Line Constructions Construction Notes Together: Construct a segment and copy it.

    You can construct a segment of any length to start. You need a guide line (a longer segment) to copy your segment onto.

    Together: Construct an angle and copy it.

    You can construct an angle of any measure. You need a guide line (that wil l be one ray of your new angle) to get started. One endpoint wil l be the vertex of your new angle.

  • Together: Construct a segment and its perpendicular bisector.

    You can construct a segment of any length to start. You need to set your compass to more than half the length of your segment.

    Together: Construct an angle and its bisector.

    You can construct any angle to start. You will draw FOUR arcs: one through each side of the angle, two in the interior of the angle.

    Together: Construct a l ine and a l ine parallel to it through a given point.

    Construct a l ine m and a point P not on the l ine. Construct a l ine n that intersects your first l ine and goes through P. This wil l be your transversal. Copy the angle formed m and n to have a vertex at P. You have constructed congruent corresponding angles.

  • 1. Construct a segment which is a copy of .

    2. Construct a segment JK which is double the length of .

    You will need a long guide line to start.

    3. Construct a segment MN such thatMN = AB+EF

    You will need a long guide line to start.

    Triangle and Polygon Constructions Construction Instructions

    4. Construct an equilateral triangle such that each side length is equal to that of segment .

    Start with just one side of the triangle.

    It will be a copy of .

    GH CD

    AB

    GHICD CD

  • 5. Construct a copy of triangle and call it

    Start by copying just one side, which is just copying a segment.

    6. Construct a triangle such that AB = RS, CD = ST, and EF = RS

    Construct a triangle out of the three reference segments.

    7. Construct an equilateral hexagon with sides all congruent to .

    XYZ UVW

    RST

    CD

  • Constructions with Perpendicular and Parallel Lines Constructions Instructions

    8. Construct a copy of , then construct is perpendicular bisector.

    9. Construct a copy of and put a point H somewhere near the segment, but not on it. Create a

    line perpendicular to that goes through point H.

    This one is a lot like constructing a perpendicular bisector.

    10. Construct a copy of and put a point K somewhere near the segment, but not on it. Create a

    line parallel to that goes through point H.

    Construct a line so that it intersects

    and has K on the line. This will be your transversal.

    Copy the angle formed by and your line to have its vertex at K.

    EF

    CD

    CD

    CD

    CDCD

    CD

  • Angle Constructions Constructions Instructions

    11. Construct a copy of

    12. Construct an angle that is double the angle measure of

    Construct a copy of , and then another copy of it adjacent to your first one.

    13. Construct an angle that is half the angle measure of

    Bisect , then copy one of the small angles.

    PQR

    MNOPQR

    PQR

    STUPQR

    PQR