Question

Answer these for 22 points

Answer 1

7. Slope of AD = 4/16 = 1/4

8. ΔAEC = 3/12 = 1/4
.. ΔDFB = 2/8 = 1/4

9. The angles at E, G, and F are right angles. Lines CE and BF are parallel, so the alternate interior angles at B and C where the transversal AD crosses them are equal. The triangles of interest are similar by AA~.

10. See problem 7. The ratio is the same.

11. Hard to tell what rule they want you to state. Every axis-aligned right triangle with its hypotenuse on AD will have the same ratio of side lengths. (That's one of the features of the graph of a line. It has the same slope everywhere, measured over any distance.)