Thinking About How to Prove Triangles are Congruent - SSS
Given: [math]AC\cong BD[/math] and [math]AB\cong CD[/math][br]Prove: [math]\bigtriangleup ABC\cong\bigtriangleup DCA[/math]
See the two triangles
Click the red triangle in the toolbar above and use the polygon tool to shade one of the two triangles. You will need to click all three points and then click back on the point you started at (4 clicks total) Does it look congruent to the other triangle? Why or why not?
Congruent Side Lengths
On the toolbar, click the angle with the red arc and the [math]\alpha[/math] next to it. Select the option "Distance or Length". Measure the given side lengths to show they are congruent by clicking on the endpoints of each segment. What are their lengths? Are they congruent?
How many pairs of congruent side lengths do we have? How many do we need for Side-Side-Side?
What is the third side of each triangle? Is it the same length in each triangle? If so, how long is it?
Bonus Question
What do we call the property where if two triangles share the same side then that side must be congruent to itself?
Congruent Triangles
Are the two triangles congruent? How do you know? [br]