G.2.4 Triangle Congruence
I have drawn triangle ABC. Triangle ABC has 6 specific measurements: 3 specific side lengths and 3 specific angle measures. Your task is to recreate my hidden triangle.
Here is where it gets a little tricky - I am only going to give you some of those 6 specific measurements.
The purpose of the activities below is to determine what is the least amount of information I can give you to construct a triangle that will be congruent to my original triangle.
To do this activity we are using a feature of GeoGebra called sliders. The sliders will allow you to "slide" both angle measures and side lengths to set their size. Once you have moved the sliders to fit the given criteria, try and move other parts of the triangle.
After everyone has had a chance to make a triangle with the given criteria, we'll compare to see if the given information was enough to make everyone's triangles the same as mine.
Attempt #1...one piece of given information
For this first drawing I am going to give you one side length.
Draw triangle ABC with the given measure:
AB= 6.3
Move the red slider so that side AB has length 6.3, then see if you can move any other parts of the triangle.
Attempt #2...two pieces of given information
For this next drawing I am going to give you one side length and one angle measure.
Draw triangle ABC with the given measures:
AB = 6.3
angle CAB = 54 degrees
Move the red slider so that side AB has length 6.3 and move the green slider so that angle CAB is 54 degrees; then see if you can move any other parts of the triangle.
Attempt #3...two pieces of given information
For this next drawing I am going to give you two angle measures (really this is 3 angles, because when I give you two angles of a triangle, you know what the third angles is).
Draw triangle ABC with the given measures:
angle CAB = 54 degrees
angle CBA = 58 degrees
Move the green slider so that angle CAB is 54 degrees and move the purple slider so that angle CBA is 58 degrees; then see if you can move any other parts of the triangle.
Attempt #4...three pieces of given information
For this next drawing I am going to give you two side lengths and the included angle measure (an included angle means that it is inbetween the 2 given sides)
Draw triangle ABCwith the given measures:
AB = 6.3
BC = 5.5
angle CBA = 58 degrees
Move the red slider so that side AB is 6.3, move the blue slider so that side BC is 5.5, and move the purple slider so that angle CBA is 58 degrees; then see if you can move any other parts of the triangle.
SAS
Attempt #5...three pieces of given information
For this next drawing I am going to give you three side lengths.
Draw triangle ABCwith the given measures:
AB = 6.3
BC = 5.5
AC = 5.76
Move the red slider so that side AB is 6.3, move the blue slider so that side BC is 5.5, and move the orange slider so that side AC is 5.76; then see if you can move any other parts of the triangle.
SSS
Attempt #6...three pieces of given information
For this next drawing I am going to give you two angle measures and the included side length (an included side means it is inbetween the 2 given angles)
Draw triangle ABCwith the given measures:
AB = 6.3
angle CAB = 54 degrees
angle CBA = 58 degrees
Move the red slider so that side AB is 6.3, green slider so that angle CAB is 54 degrees and move the purple slider so that angle CBA is 58 degrees; then see if you can move any other parts of the triangle.
ASA
Attempt #7...three pieces of given information
For this next drawing I am going to give you angle measures and the non-included side length (a non-included side means that it in NOT inbetween the 2 given angles)
Draw triangle ABC with the given measures:
AB = 6.3
angle CBA = 58 degrees
angle ACB = 68 degrees
Move the red slider so that side AB is 6.3, move the purple slider so that angle CBA is 58 degrees and move the pink slider so that angle ACB is 68 degrees; then see if you can move any other parts of the triangle.
AAS
Attempt #8...three pieces of given information
For this next drawing I am going to give you side length and the non-included angle measure (a non-included angle means that it in NOT inbetween the 2 given sides)
Draw triangle ABC with the given measures:
angle BAC = 54 degrees
AB = 6.3
BC = 5.5
Move the green slider so angle BAC is 54 degrees and move the red slider so that side AB is 6.3. Then, swivel side BC, which is set to 5.5, until it matches up with the ray that comes from point A.
SSA
Attempt #9...three pieces of given information
For this last drawing we are working with a brand new trianlge. I am going to give you a more specific version of two side lengths and the non-included angle measure. The angle needs to be 90 degrees.
Draw triangle ABCwith the given measures:
angle CAB = 90 degrees
AB = 5.5
BC = 6.7
Angle CAB is set to 90 degrees. Move the red slider so that side AB is 5.5 and move the blue slider so that side BC is 6.7; then see if you can move any other parts of the triangle.