G.2.4.2 What Information Do I Need?
- Author:
- Katie Akesson, LeonMilewski
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 new 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:
Side 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:
Side 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
OK, 2 pieces of information didn't work, let's try three.
For this next drawing I am going to give you two side lengths and one angle measure (the non-included angle - meaning it's NOT the angle that is inbetween the 2 given sides).
Draw triangle ABC with the given measures:
angle CAB = 54 degrees
side AB = 6.3
side BC = 5.5
Move the green slider so that angle CAB is 54 degrees, move the red slider so that side AB has length 6.3, and move point C until side BC has length 5.5; then see if you can move any other parts of the triangle.
SSA
Attempt #5...three pieces of given information
OK, those 3 pieces of information almost worked...we're getting closer, let's try a different 3 pieces.
For this next drawing I am going to give you two side lengths and one angle measure (the included angle - meaning it's the angle that is inbetween the 2 given sides).
Draw triangle ABC with the given measures:
angle ABC = 58 degreesside AB = 6.3
side BC = 5.5
Move the purple slider so that angle ABC is 58 degrees, move the red slider so that side AB has length 6.3, and move blue slider until side BC has length 5.5; then see if you can move any other parts of the triangle.
SAS
Attempt #6...three pieces of given information
Let's try and see if three different pieces of information will work.
For this next drawing I am going to give you three side lengths.
Draw triangle ABC with the given measures:
side AB = 6.3
side BC = 5.5
side AC = 5.76
Move the red slider so that side AB has length 6.3, move the blue slider so that side BC has length 5.5, and move the pink slider so that side AC has length 5.5; then see if you can move any other parts of the triangle.
SSS
Attempt #7...three pieces of given information
Let's try this again and see if three different pieces of information will work.
For this next drawing I am going to give you three side lengths.
Draw triangle ABC with the given measures:
Angle CAB = 54 degrees
Angle CBA = 58 degrees
AB = 6.3
Move the red slider so that side AB has length 6.3, 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.