Math+10

Math 10 -
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**__6.7 CONSTRUCTIONS__ Click on the heading of the instructions to see a video of the construction.**
=[|1. Copy a segment]= Directions: 1. If a reference line does not already exist, draw a reference line with your straightedge upon which you will make your construction. Place a starting point on the reference line. 2. Place the point of the compass on point A. 3. Stretch the compass so that the pencil is exactly on B. 4. Without changing the span of the compass, place the compass point on the starting point on the reference line and swing the pencil so that it crosses the reference line. Label your copy. Your copy and line segment AB are congruent (equal in length). Explanation of construction: The two line segments are the same length, therefore they are congruent.

=[|2. Copy an Angle]= Directions: 1. If a reference line does not already exist, draw a reference line with your straightedge upon which you will make your construction. Place a starting point on the reference line. 2. Place the point of the compass on the vertex of angle BAC (point A). 3. Stretch the compass to any length so long as it stays ON the angle. 4. Swing an arc with the pencil that crosses both sides of angle BAC. 5. Without changing the span of the compass, place the compass point on the starting point of the reference line and swing an arc that will intersect the reference line and go above the reference line. 6. Go back to angle BAC and measure the width (span) of the arc from where it crosses one side of the angle to where it crosses the other side of the angle. 7. With this width, place the compass point on the reference line where your new arc crosses the reference line and mark off this width on your new arc. 8. Connect this new intersection point to the starting point on the reference line. Your new angle is congruent to angle BAC. Explanation of construction: When this construction is finished, draw a line segment connecting where the arcs cross the sides of the angles. You now have two triangles that have 3 sets of congruent (equal) sides. SSS is sufficient to prove triangles congruent. Since the triangles are congruent, any leftover corresponding parts are also congruent - thus, the angle on the reference line and angle BAC are congruent.