Lesson 2 Do You See What I See? Develop Understanding


Consider the given statements and fill in the blank with something that makes sense. The first comparison demonstrates a relationship and the second comparison has a blank for you to fill in based on the relationship provided. There may be more than one logical way to fill in the blank.

For example, in the statement, “Foot is to boot as hand is to .” You would consider the first part of the statement “foot is to boot” and think about the relationship. It is apparent that a foot can go in or wear a boot. Logically then it would make sense to fill in the blank with “glove” since a hand can go in or wear a glove.


Pencil is to writing as violin is to


Fishing is to lake as soccer is to


Equal slopes is to parallel lines as negative reciprocal slopes is to


Hexagon is to triangle as decagon is to


Subtraction is to addition as division is to


Congruent is to shapes as equal is to

Decide if the following statements provide a true logical conclusion or if the statement is false. If false, provide a counterexample.


An acute triangle only needs to have one acute angle.


If a rectangle is cut in half then there will be two triangles.


If you have supplementary angles, they will create a straight line.


If you have complementary angles, they will add up to .


Many diagrams have a history and progression to the way they are created. For each diagram, list the steps in the order that you think they occurred to make the diagram. Then make a conjecture about the piece of the diagram indicated. Consider using a compass and straightedge to reconstruct the diagram as you work. Finally, write an argument that can be used to justify to someone that your conjecture would be true.



Circle A, Circle C, and Circle D intersect such that quadrilateral ACDE is formed and point E lies on both Circle D and Circle C.

List the steps to create the diagram:

Conjecture about quadrilateral :




Circle A and Circle C overlap such that quadralateral ABCD is formed. Point E and Point F lie on both Circle A and Circle C. A line segment connects Points, F, D, G, B, E. Point G also resides on line segment AC and creates Circle G through points A,B,C,D.

List of steps to create the diagram:

Conjecture about quadrilateral :


Examine the diagram and add any information that is given to the diagram. Make a plan for finding the value of . Follow your plan. Show your work, justifying the results.



A right triangle with hypotenuse of 26 cm, shorter side 10 cm, and longer side x cm.



A straight line divided into three angles. Angle ABC is formed by Point B being on the straight line. AB and BC are line segments and sides of Angle ABC. Angle ABC is not labeled, the angle between Angle ABC and the line B on the left is labeled with an x and the angle between Angle ABC and the line B on the right is labeled 2x.


Given: , , and are right triangles.

Triangle ABD and Triangle BDC shares line segment BD. A line segment connects Point C and Point E on the line segment BD. Line segment AD is 15 m, Line segment AB is 8 m, line segment BC is 14 m, Line segment EC is 6 M, and line segment DC is labeled x.



  1. Label points , , and with the correct ordered pairs.

  2. Translate down and right . Label the image as and include the new ordered pairs.

  3. Draw , , and . What is the slope of each of these line segments?

  4. Reflect across the line. Label the image . Include the new ordered pairs.

  5. Draw and . Why don’t you need to draw ? What is the relationship between and to the line?

  6. Rotate about the point . Label the image . Include the new ordered pairs.

A coordinate plane with x- and y-axis with 1-unit increments. Triangle ECD contains the points E (-3,3) D(0,4), and C (-4,0). x–5–555y–5–55500