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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.