build SSS, SAS, ASA historicsweetsballroom.com Topical summary | Geometry summary | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts

 Use only your compass and straight leaf when drawing a construction. No free-hand drawing!

 You currently know every one of the constructions the are supplied to prepare the constructions because that SSS, SAS, and ASA. Simply remember to attract the last 2 constructions in the needed order.You are watching: How to construct a congruent triangle

You may run right into a "trick" concern where the offered segments will certainly NOT kind a triangle. Remember the the sum of the lengths of any type of two political parties of a triangle must be better than the size of the 3rd side. If this relationship does no occur, you will certainly NOT have the ability to draw a triangle.

This SSS building and construction will it is in to "copy a segment" 3 times.

 Steps: 1) draw a referral line, if one is no given, and also place a starting dot (A). 2) Copy segment c. With compass, measure up the span of segment c. It is usually much easier to start with the longest segment. (Place a small arc to show that you measured the segment.) 3) place compass point on A and transfer this expectations with a little arc crossing the reference line. (Label B.) 4) Copy segment b. With compass, measure expectations of segment b. 5) ar compass point on A and also transfer the expectations of b making an arc above the referral line. 6) Copy segment a. With compass, measure span of segment a. 7) location compass allude on B and transfer the expectancy of a do an arc above the referral line, intersecting v previous arc. (Label C.) 8) connect points A, B and C because that ΔABC. notification the labeling in this construction. the is customary to brand vertices with capital letters and also segments with single small case letters. Also an alert that the little case a is put opposite peak A, and so on.

every triangles constructed with these three segments will certainly be congruent.

 Given: 2 segments and also one edge Construct: a triangle such that the angle will be included between the two offered segments (sides)

The SAS order the the building will it is in "copy a segment", complied with by "copy one angle", adhered to by "copy a segment" again.

 Steps: 1) attract a reference line, if one is not given, and place a starting dot (A). We will certainly be copying our angle"s vertex at this point. 2) Copy segment c. With compass, measure the span of segment c. 3) location compass point on A and also transfer this span with a small arc cross the referral line. (Label B.) 4) Copy edge A. Place compass in ~ vertex that the given angle. Swing an arc cross both political parties of the angle. Store this compass span. 5) Without changing compass span, location compass allude at A on the reference line and also draw this arc sufficiently large and crossing the referral line. 6) Return to the provided angle and measure span throughout the arc through the compass. 7) Without transforming compass span, deliver this expectancy to her arc on the referral line, and also draw a beam from A v the suggest of intersection. 8) Copy segment b. With compass, measure the span of segment b and mark it off on the new ray developed in your construction. (Label C.) draw ΔABC. It is useful to mental this building in the SAS order: copy next copy edge copy next All triangles created with these sides and this angle, in this bespeak pattern, will be congruent.Given: 2 angles and also one side Construct: a triangle such that the side will certainly be included in between the two given angles

The ASA order of the building will be "copy one angle", complied with by "copy a segment", adhered to by complied with by "copy an angle" again.