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WEEK 11 (assignments 37-39)
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
11/9 homework (#37)
Construct three congruent triangles (Image) from three originals Given:
a) Right Triangle
b) Obtuse Triangle
c) Acute Triangle
ec) Isosceles Triangle
Copy as many parts as necessary to be sure that the Image is congruent to the
original. Label the image triangle with new points and make a triangle congruence
statement
11/10 homework (#38)
Construction four congruent triangles using SSS from four originals:
(1) Right Triangle
(2) Obtuse Triangle
(3) Acute Triangle
(4) Isosceles
Construction four congruent triangles using SAS from the same four type of
originals: (5-8)
Label the image triangle with tic marks showing the congruent parts that were
copied, label the new points and make a triangle congruence statement
11/12 homework (#39)
Construction four congruent triangles using ASA from four originals:
(1) Right Triangle
(2) Obtuse Triangle
(3) Acute Triangle
(4) Isosceles
First construct four right triangles on the left “original” side leaving the left side to construct a congruent triangle
Using a segment AB of three lines, make the following right triangles and then
use HL to make image triangles with that are congruent to the originals
(5)
(6)
(7)
(8)
Leg:
Leg:
Leg:
Leg:
HI=AB and Hyp: GH=2AB, construct ΔGHI
JL=1½ AB and Hyp: JK=2½ AB, construct ΔJKL
NO=½ AB and Hyp: MN=1½ AB, construct ΔMNO
PO=½ AB and Hyp: PQ=2AB, construct ΔOPQ
Second construct four congruent triangles on the right “image” marking the congruent parts, using new letters and making a Δ statement in a box
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.
(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.