You will use [math]\Delta[/math]ABC for all parts of Investigation 1.
In the figure below, [math]\Delta[/math]A'B'C' is the image of [math]\Delta[/math]ABC after a dilation by scale factor d. You can change the scale factor by moving the slider. [br]1: Use the perpendicular line tool to construct the altitudes through B and B'. Use the point and length tools to measure the length of each altitude.[br]2: Use the midpoint and segment tools to construct the medians from points A and A'. Use the length tool to measure the length of each median.[br]3: Use the angle bisector tool to construct the bisectors of [math]\angle[/math]C and [math]\angle[/math]C'. Use the point and length tools to measure the length of each angle bisector.
Move the slider to your chosen scale factor (not 1). Calculate the ratio of the length of the altitude through point B' to the length of the altitude through point B.[br][br]How does the ratio of these two lengths compare to the scale factor?
The ratio of the altitudes is equal to the scale factor.
Calculate the ratio of the length of the median through point A' to the length of the median through point A.[br][br]How does the ratio of these two lengths compare to the scale factor?
The ratio of the medians is equal to the scale factor.
Calculate the ratio of the length of the angle bisector through point C' to the length of the angle bisector through point C.[br][br]How does the ratio of these two lengths compare to the scale factor?
The ratio of the angle bisectors is equal to the scale factor.
There are two parts to investigation 2. Carefully follow the instructions below to complete the conjecture.
Use the angle bisector tool to construct the bisector of [math]\angle[/math]A.[br]Create a point where the angle bisector intersects segment BC, and label it X.[br]Use the length tool to find the lengths CX and BX. [br]
How does the ratio of sides AB and AC compare to the ratio of BX and CX?
Use the angle bisector tool to construct the bisector of [math]\angle[/math]A.[br]Create a point where the angle bisector intersects segment BC, and label it X.[br]Use the length tool to find the lengths CX and BX.
How does the ratio of sides AB and AC compare to the ratio of BX and CX?