Copy line Segment or edge rebab.net Topical overview | Geometry summary | MathBits" Teacher sources Terms that Use call Person: Donna Roberts
| ||Use only your compass and also straight sheet when illustration a construction. No free-hand drawing!|
The constructions connected with copy a segment and also copying one angle need that you have actually a "place" to begin your copy. It is customary to attract a right line upon which friend then produce your copy. Together a heat is dubbed a "reference line".
Given: (a heat segment) Construct: a heat segment congruent to .
You are watching: How to construct a congruent segment
(make a copy the the segment).
STEPS: 1. utilizing a straightedge, attract a recommendation line, if one is no provided. 2. Draw a dot on the referral line to note your beginning point because that the construction. 3. Place the allude of the compass on suggest A on the offered figure. 4. Stretch the compass so that the pencil is specifically on B. Do a small arc through B.(This tiny arc will present that you measured the length of the segment with your compass.) 5. Without changing the span of the compass, ar the compass suggest on the starting point (dot) top top the reference line and swing the pencil to produce an arc crossing the recommendation line. 6. brand your copy.
Proof of Construction: The compass was used as a measuring tool to achieve (and copy) the size of the offered segment. Since the given segment and the copy room the same length, the segments are congruent. Note: You may likewise think of the length from A to B together being the radius that a circle with facility at A. By copying the circle in ~ A", the radii segments will certainly be congruent.
Copy one angle
Given: ∠ABC Construct: an edge congruent to ∠ABC. (make a copy that the angle)
STEPS: 1. Using a straightedge, attract a reference line, if one is not provided. 2. ar a dot (starting point) top top the reference line. 3. place the point of the compass ~ above the crest of the provided angle, ∠ABC (vertex at allude B). 4. Stretch the compass to any kind of length that will stay "on" the angle. 5. Swing one arc therefore the pencil will certainly cross BOTH political parties (rays) of the angle. 6. Without transforming the size of the compass, ar the compass point on the starting point (dot) ~ above the referral line and swing one arc that will intersect the referral line and go over the recommendation line. 7. Go ago to the offered angle ∠ABC and measure the expectations (width) of the arc from whereby it crosses one side of the edge to whereby it crosses the other side that the angle. (Place a little arc to show you measure up this distance.) 8. Using this width, location the compass suggest on the referral line whereby the previous arc the cross the referral line and also mark turn off this new width top top your new arc. 9.
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connect this new intersection allude to the beginning point (dot) ~ above your reference line. 10. label your copy.
Proof of Construction: When your construction is finished, attract line segment connecting where the first arcs cross the political parties of the angles. We know these lengths space the very same in both drawings due to the fact that they stand for the measured spans that the same arcs. These addition of this segments will create two triangle that have actually 3 sets of congruent (equal) sides. Because the triangles space congruent by SSS and also any leftover matching parts will likewise be congruent (by CPCTC), we understand that ∠ABC is congruent come ∠A"B"C". (Note: These triangles are not have to ΔABC and also ΔA"B"C", because the an initial arc in the building need not pass with A and/or C on the offered angle.)