True or false? Justify your reasoning.

b. If two triangles are congruent, they are similar.

A student claims that if one angle in an isosceles triangle is congruent to an angle in another isosceles triangle, then the triangles are similar. How do you respond?

Bob says that if each right triangle has an acute angle with the same measure, the triangles are similar. How do you respond?

If two isosceles triangles have non-base angles of $40^\circ$, are they similar? Justify your answer.

To find the height of a pole, Elka lays a mirror on the level ground 20 ft from the base of the pole. She moves back away from the mirror until she can exactly see the top of the pole. If she backed away 5.5 ft and her eyes are 5 ft above the ground, how tall is the flag pole?

Which of the following figures are always similar?
a. Any two rectangles in which the diagonal in one is twice as long as in the other.
b. Any two rhombuses
c. Any two circles
d. Any two regular polygons
e. Any two regular polygons with the same number of sides

When completed, the Crazy Horse Monument in South Dakota will be 563 ft high. The monument is based on a 16-foot-tall scale model of the structure. What is the scale used in the construction?

School pictures come in 8 in. by 10 in., 5 in., by 7 in., and wallet size $2\frac 1 4$ in. by $3 \frac 1 4$ in. Are any of these sizes similar to each other? Why?

Determine whether the following represents a population or a sample.

a school lunch survey that asks every fifth student that enters the lunchroom

For this item, draw a line through the points on your graph.

Use the data in the table, the slope determined in part a, and the graph to determine the y-intercept of the line through the data points. Describe the meaning of the y-intercept in this problem situation.

If a trend line has equation y = 3.2x - 0.11, what y-value would you expect to obtain when x has the following values?
a. 1
b. 0
c. 10
d. 20.3

Jacquie argued that scatterplots had little value because rarely does a single trend line fit the data. How do you respond?

Merle says that there is no reason to practice drawing graphs because spreadsheets can be used to draw any images desired. How do you respond?

If a trend line has equation y = 0.0001x + 12, what could you say about the data?