SAS Exploration

Author:: kjordanlghs, dgibson

Topic:: Geometry

In the exploration below, three parts of the disassembled figure are fixed so their measures will always be identical to three parts of the shaded triangle. You are able to manipulate the other sides and angles of the disassembled figure. Move the points of the disassembled figure around to try to form a triangle. Is it possible to make the disassembled figure into a triangle that is different than the first? When you've made your conclusion, answer the questions below.

Describe the parts that always have the same measure in both figures.

Select all that apply

A
three sides
B
three angles
C
two angles and one side
D
two sides and one angle

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Describe the location of the angle that is the same in both figures.

Select all that apply

A
There is no angle that is always the same in both triangles
B
It is the angle that is formed by the two sides whose lengths do not change

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In the SSS exploration you did earlier, you were able to move one triangle on top of the other triangle to convince yourself the two triangles were congruent. This sketch does not allow you to do that. So how are you able to be convinced that the triangles are in fact congruent?

Select all that apply

A
I can't be convinced because they're not congruent.
B
When I formed the triangle from the disassembled figure I noticed that all the sides lengths of the two triangles matched up and all the angles matched up, so all 6 parts of the one triangle were the same as the 6 parts of the other triangle. And if all 6 parts of one triangle are the same as all 6 parts of another, then the triangles are congruent.
C
When I formed the triangle from the disassembled figure I noticed that all three lengths of the triangle I created were the same as the 3 lengths of the shaded triangle, and the SSS exploration that I did previously tells me that these two triangles have to be identical if their 3 sides lengths match up.

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Which sentence below do you think best summarizes what you observed in this investigation?

Select all that apply

A
If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
B
If the three angles of one triangle are congruent to the three angles of another triangle then the triangles are congruent.
C
If two sides and the angle that they form (called the included angle) in one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

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The name of this investigation is SAS. What do you think SAS stands for?

Select all that apply

A
Socks And Shoes
B
Soup And Salad
C
Special Air Service
D
Side Angle Side

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It is not a coincidence that the letter A is SAS occurs in between the S's. What is it about the configuration of the congruent parts of these triangles that you think explains why this abbreviation is spelled the way it is?

Select all that apply

A
The angle that is congruent in both figures is the angle that is in between the pair of congruent sides in each figure
B
They put the A in the middle because if they put it at the beginning it would spell a naughty word.
C
They put the A in the middle because if they put it at the end, it would spell a naughty word backwards

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SAS Exploration

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