Download Constructing Congruent Triangles

Constructing Congruent Triangles
Videos:
(1) Triangle Congruence (Definition):
http://teachertube.com/viewVideo.php?video_id=3709&title=Congruence__Triangles
Old videos (need to re-find)
(2) SSS Postulate
http://www.teachertube.com/view_video.php?viewkey=e7cb7f4ddd97326c843c
(3) SAS and ASA Postulates
http://www.teachertube.com/view_video.php?viewkey=fdb2463605f6e88a3a81
(4) AAS Theorem
http://www.teachertube.com/view_video.php?viewkey=c53b566b6c107b19f4bb
(5) HL Theorem
http://www.teachertube.com/view_video.php?viewkey=da8082f6fbbb317ab612
Each construction has an original triangle and an image ray on which to construct a congruent
triangle. For every construction, there should be three parts labeled as congruent between the
original and the image. ONLY THREE PARTS should be labeled in pairs between the
original and the image. These are the parts that were used in the specific construction (SSS,
SAS, ASA, or in the case of HL, you also need to identify the right angles)
(1)
(2)
(3)
(4)
SSS Congruent Triangle construction
Copy the length of the longest side from the original to your image ray.
From one endpoint of the image side, make an arc the length of one of the remaining
sides of the original
From the other endpoint of the image side, make an arc the length of the last remaining
side such that it intersects the arc made in step 2 (note: you may need to extend the
arc in step 2 to intersect this arc)
Label all the new points, make tic marks on the congruent sides, THEN box a triangle
congruence statement
NOTE: there should only be three parts marked on both the original and the image.
(1)
(2)
(3)
(4)
SAS Congruent Triangle construction
Copy any angle from the original to your image ray.
Along one side of the image angle, make an arc the length of one of the sides of the
original angle.
Along the other side of the image angle, make an arc the length of the other side of
the original angle.
(note: you may need to extend the sides of the image angle in step 1 to intersect
either of these arcs made in steps 2 or 3)
Label all the new points, make tic and/or arc marks on the congruent angle and sides,
THEN box a triangle congruence statement
NOTE: there should only be three parts marked on both the original and the image.
(1)
(2)
(3)
(4)
(5)
(6)
ASA Congruent Triangle construction
Copy any side from the original to your image ray (recommend the longest side).
Make congruent measuring arcs from both endpoints of the original side and both
endpoints of the image side. (four total, with the same radius)
Copy the span of one original angle (from one endpoint of the side) to one measuring
arc on the image. Complete this angle by drawing the side. Mark the congruent angles.
Copy the span of other original angle (from the other endpoint of the side)to the last
measuring arc on the image. Complete this angle by drawing the side. Mark the
congruent angles.
Mark the congruent side between the two angles with tics, and Label the intersection of
the two sides as your last point (note: you may need to extend the sides of the image
angles in steps 3 and 4 to intersect)
Label all the new points, make tic and/or arc marks on the congruent angles and sides,
THEN box a triangle congruence statement
NOTE: there should only be three parts marked on both the original and the image.
HL Congruent Triangle construction (original Right Triangle)
(1)
(2)
(3)
(4)
First make a right angle on the image by pulling a perpendicular from a point on a line
(Using the length of a leg of the original triangle as your semicircle will allow you
to skip the next step)
Copy the length of a leg from the original to one of the sides of the right angle in
your image.
From the endpoint of the leg not at the right angle, make an arc the length of the
Hypotenuse such that it intersects the other leg coming from the right angle (note: you
may need to extend the other leg to intersect this arc)
Label all the new points, box your right angle, and make tic marks on the congruent leg
and hypotenuse, THEN box a triangle congruence statement
NOTE: there should only be three parts marked on both the original and the image.