In triangles [math]GBD[/math] and [math]KHI[/math]:[br][list][*]Angle [math]GBD[/math] is congruent to angle [math]KHI[/math].[/*][*]Segment [math]BD[/math] is congruent to segment [math]HI[/math].[/*][*]Segment [math]DG[/math] is congruent to segment [math]IK[/math].[/*][/list]
Use the applet below to make a triangle using the given angle and side lengths so that the given angle is not between the 2 given sides. Try to make your triangle different from the triangles created by the other people in your group.[br][list][*]Angle: [math]40^{\circ}[/math][/*][*]Side length: 6 cm[/*][*]Side length: 8 cm[/*][/list]
[list][*]For each set of information, use the applet below to make a triangle using that information.[/*][*]If you think you can make more than one triangle, make more than one triangle.[/*][*]If you think you can’t make any triangle, note that.[/*][/list]
[size=150]Now use the straightedge and compass to construct the midpoint of [math]CD[/math]. Label that midpoint [math]M[/math].[/size][br][br]Explain why triangle [math]ABM[/math] is a right triangle.[br]
Explain why knowing the angle at [math]A[/math] and the side lengths of [math]AB[/math] and [math]BC[/math] was not enough to define a unique triangle, but knowing the angle at [math]A[/math] and the side lengths of [math]AB[/math] and [math]BM[/math] would be enough to define a unique triangle.[br]