Success Criteria: I can use special geometric tools to make a figure that is congruent to an original figure without measuring I can apply this method.

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Presentation transcript:

Success Criteria: I can use special geometric tools to make a figure that is congruent to an original figure without measuring I can apply this method that is more accurate than measuring Today 1. Do Now 2. Lesson Check HW #6 Do Now Find the following measures using the image.

Definitions Construction – Use a straight edge and a compass to make geometric figures Straightedge – is a ruler with no marking on it Compass – Geometric tool used to draw circles and parts of circles called arcs Perpendicular Lines-two lines that intersect to form right angles. Perpendicular bisector-of a segment is a line that is perpendicular to the midpoint

Congruent segment

Congruent Angles

Perpendicular Bisector

Angle Bisector

Construct a triangle given three line segments

Assignment #6 pg 46 #7, 11, 13, 14, 16

Step 2: Open the compass to the length of KM. Construct TW congruent to KM. Step 1: Draw a ray with endpoint T. Step 3: With the same compass setting, put the compass point on point T. Draw an arc that intersects the ray. Label the point of intersection W. TW KM

Construct Y so that Y G. Step 1: Draw a ray with endpoint Y. Step 3: With the same compass setting, put the compass point on point Y. Draw an arc that intersects the ray. Label the point of intersection Z. Step 2: With the compass point on point G, draw an arc that intersects both sides of G. Label the points of intersection E and F. 75°

(continued) Step 4: Open the compass to the length EF. Keeping the same compass setting, put the compass point on Z. Draw an arc that intersects the arc you drew in Step 3. Label the point of intersection X. Y G Step 5: Draw YX to complete Y.

Start with AB. Step 2: With the same compass setting, put the compass point on point B and draw a short arc. Without two points of intersection, no line can be drawn, so the perpendicular bisector cannot be drawn. Prove by construction why you cannot construct a perpendicular bisector with a compass opening less than AB Step 1: Put the compass point on point A and draw a short arc. Make sure that the opening is less than AB. 1212

–3x = –48 Subtract 4x from each side. x = 16 Divide each side by –3. m AWR = m BWRDefinition of angle bisector x = 4x – 48Substitute x for m AWR and 4x – 48 for m BWR. m AWB = m AWR + m BWRAngle Addition Postulate m AWB = = 32Substitute 16 for m AWR and for m BWR. Draw and label a figure to illustrate the problem WR bisects AWB. m AWR = x and m BWR = 4x – 48. Find m AWB. m AWR = 16 m BWR = 4(16) – 48 = 16 Substitute 16 for x.

Step 1: Put the compass point on vertex M. Draw an arc that intersects both sides of M. Label the points of intersection B and C. Step 2: Put the compass point on point B. Draw an arc in the interior of M. Construct MX, the bisector of M.

Step 4: Draw MX. MX is the angle bisector of M. (continued) Step 3: Put the compass point on point C. Using the same compass setting, draw an arc in the interior of M. Make sure that the arcs intersect. Label the point where the two arcs intersect X.

You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge.

Example 2: Copying a Segment Sketch, draw, and construct a segment congruent to MN. Step 1 Estimate and sketch. Estimate the length of MN and sketch PQ approximately the same length. PQ

Example 2 Continued Sketch, draw, and construct a segment congruent to MN. Step 2 Measure and draw. Use a ruler to measure MN. MN appears to be 3.5 in. Use a ruler to draw XY to have length 3.5 in. XY

Example 2 Continued Sketch, draw, and construct a segment congruent to MN. Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to MN. A ruler shows that PQ and XY are approximately the same length as MN, but ST is precisely the same length.

Check It Out! Example 2 Sketch, draw, and construct a segment congruent to JK. Step 1 Estimate and sketch. Estimate the length of JK and sketch PQ approximately the same length.

Check It Out! Example 2 Continued Step 2 Measure and draw. Use a ruler to measure JK. JK appears to be 1.7 in. Use a ruler to draw XY to have length 1.7 in. Sketch, draw, and construct a segment congruent to JK.

Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to JK. A ruler shows that PQ and XY are approximately the same length as JK, but ST is precisely the same length. Check It Out! Example 2 Continued Sketch, draw, and construct a segment congruent to JK.