scissors glue/tape a set of triangle/method sheets roll paper or construction paper to paste the cards on to
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- Loren Marshall
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2 Materials: Each student (or group of students) will need: scissors glue/tape a set of triangle/method sheets roll paper or construction paper to paste the cards on to Objectives (The Student Will Be Able To): Identify when two angles are being marked congruent Solve proportions to determine if two sides are proportional Rotate figures mentally or through redrawing to be able to match up corresponding sides Identify when the SSS, SAS, or AA method is being illustrated and used to prove two triangles similar Determine when two triangles are not similar even though the original diagram may lead them to a believe a method may apply Launch: We have spent time discussing the different methods of proving triangles similar. Today we are going to eplore whether or not you can recognize them in action. Procedure and Monitoring: 1. Open with a short review of: The three methods of proving triangles similar- - have students come up and draw them, or have students verbally brainstorm them.
3 Break the students into groups of no more than four and hand out the necessary materials. o Remind them write the methods in the boes net to the triangles before they start cutting them apart and pasting them down. o Remind them to set-up and solve the proportions and solve for missing angles before they start cutting them apart and pasting them down o Have them eplain WHY two triangles aren't similar if that is the heading they put them under Once the students have finished labeling all the methods they cut the pieces apart and paste them under the correct method headings. You can post the roll paper on the walls and do a gallery walk so that students can see what others did. Bring the class back together and discuss any triangles that multiple students had the same misconceptions about.
4 Sides are in proportion, angle between sides cong., so similar by SAS SAS # # 7 Two pairs of angles cong., so similar by AA AA
5 #3 Three pairs of sides are in proportion, so similar by SSS SSS # No two pairs of angles are cong., not enough information given to determine if sides are in proportion, so NOT SIMILAR NOT SIM. #5 Triangles are congruent, which makes the sides proportional in a 1-to-1 ratio, so similar by SSS SSS ; At least two pairs of angles are congruent, so similar by AA AA #
6 1 7 While 1 and 7 means that that the sides are proportional, the congruent angle is not between them, so they are not similar #7 NOT SIM Sides are in proportion, angle between sides cong., so similar by SAS SAS # Parallel Lines are denoted by arrow heads meaning that we are given two pairs of corresponding angles that are congruent, so similar by AA #9 AA #10 7. Sides are in proportion,., so similar by SSS SSS
7 Sides are in proportion, angle between sides cong., so similar by SAS SAS # Not all sides are in proportion, so not similar # NOT SIM. 5 Not Enough Information Given To Determine So Not Similar # NOT SIM. + Smaller triangle is equilateral with sides of "". Larger triangle is equilateral with sides of "+". Triangles will be have all sides proportional at a rate of, so similar by SSS #1 SSS
8 # # 7
9 1 # # # # 75
10 1 #7 7 # 1 3 # #
11 #11 3 # # #1 +
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