91Ó°ÊÓ

If two congruent angles are supplementary, what must be true of the two angles? Make a sketch, then complete the following conjecture: If two angles are both congruent and supplementary, then ____________________ .

Identify the statement as true or false. For each false statement, explain why it is false or sketch a counter example. The largest chord of a circle is a diameter of the circle.

Mark Twain once observed that the lower Mississippi River is very crooked and that over the years, as the bends and the turns straighten out, the river gets shorter and shorter. Using numerical data about the length of the lower part of the river, he noticed that in the year 1700 , the river was more than 1200 miles long, yet by the year \(1875,\) it was only 973 miles long. Twain concluded that any person "can see that 742 years from now the lower Mississippi will be only a mile and three-quarters long" What is wrong with this inductive reasoning?

Sketch, label, and mark the figure. Scalene obtuse triangle \(P A T\) with \(P A=3 \mathrm{cm}, A T=5 \mathrm{cm},\) and \(\angle A \quad\) an obtuse angle.

Sketch and carefully label the figure. A net for a rectangular solid with the dimensions 1 by 2 by \(3 \mathrm{cm}\).

Use inductive reasoning to find the next two terms of the sequence. $$\frac{1}{2}, 9, \frac{2}{3}, 10, \frac{3}{4}, 11,1,?,?$$

Use your ruler and protractor to draw a triangle with side lengths \(8 \mathrm{cm}\) and \(9 \mathrm{cm}\) and an angle between them measuring \(45^{\circ} .\) Explain your method. Can you draw a second triangle using the same instructions that is not congruent to the first?

Sketch, label, and mark the figure. A 3 -by-4-by-6-inch rectangular solid rests on its smallest face. Draw lines on the three visible faces to show how you can divide it into 72 identical smaller cubes.

What type (or types) of triangle has one or more lines of symmetry?

Identify the statement as true or false. For each false statement, explain why it is false or sketch a counter example. A line segment that connects any two vertices in a polygon is called a diagonal.