Fill in the missing statement and a reason in the proof of the corresponding angles theorem “It is given that AB is parallel to CD and points E, G,H, and F are collinear. The measure of EGF is 180°, by the definition of a straight angle. AGE and AGF I adjacent So the measure of AGE plus the measure of AGF equals the measure of EGF by the angle addition postulate. Then substituting for the measure of EGF it can be said that the measure of AGE plus the measure of AGF equals 180°. _, so the measure of CHE pulse the measure of AGF. The measure of AGE is equal to the measure of CHE _. Finally by the definition of congruence, AGE is congruent to CHE.”

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?