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Lesson 9Drawing Triangles (Part 1)

Let’s see how many different triangles we can draw with certain measurements.

Learning Targets:

  • Given two angle measures and one side length, I can draw different triangles with these measurements or show that these measurements determine one unique triangle or no triangle.

9.1 Which One Doesn’t Belong: Triangles

Which one doesn’t belong?

Triangles A, B, C, and D all have different angles and side lengths.

9.2 Does Your Triangle Match Theirs?

Three students have each drawn a triangle. For each description of a student’s triangle:

  1. Drag the vertices to create a triangle with the given measurements.

  2. Compare their measurements to the other side lengths and angle measures in your triangle.

  3. Decide whether the triangle you made must be an identical copy of the triangle that the student drew. Explain your reasoning.

Jada’s triangle has one angle measuring 75°.

Andre’s triangle has one angle measuring 75° and one angle measuring 45°.

Lin’s triangle has one angle measuring 75°, one angle measuring 45°, and one side measuring 5 cm.

9.3 How Many Can You Draw?

  1. Draw as many different triangles as you can with each of these sets of measurements:

    1. Two angles measure 60^\circ , and one side measures 4 cm.
    2. Two angles measure 90^\circ , and one side measures 4 cm.
    3. One angle measures 60^\circ , one angle measures 90^\circ , and one side measures 4 cm.

  2. Which sets of measurements determine one unique triangle? Explain or show your reasoning.

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Are you ready for more?

Three triangles connected at the base
In the diagram, 9 toothpicks are used to make three equilateral triangles. Figure out a way to move only 3 of the toothpicks so that the diagram has exactly 5 equilateral triangles.

Lesson 9 Summary

Sometimes, we are given two different angle measures and a side length, and it is impossible to draw a triangle. For example, there is no triangle with side length 2 and angle measures 120^\circ and 100^\circ :

In the figure a horizontal line segment is drawn and labeled 2. On the left end of the line segment, a dashed line is drawn upward and to the left. The angle formed between the dashed line and the horizontal line is labeled 120 degrees. On the right end of the horizontal line, a dashed line is drawn upward and to the right. The angle formed between the dashed line and horizontal line is labeled 100 degrees.

Sometimes, we are given two different angle measures and a side length between them, and we can draw a unique triangle. For example, if we draw a triangle with a side length of 4 between angles 90^\circ and 60^\circ , there is only one way they can meet up and complete to a triangle:

Two intersecting dotted lines form a triangle with a side length of 4 and angles of 60 and 90 degrees.

Any triangle drawn with these three conditions will be identical to the one above, with the same side lengths and same angle measures.

Lesson 9 Practice Problems

  1. Use a protractor to try to draw each triangle. Which of these three triangles is impossible to draw?

    1. A triangle where one angle measures 20^\circ and another angle measures 45^\circ
    2. A triangle where one angle measures 120^\circ and another angle measures 50^\circ

    3. A triangle where one angle measures 90^\circ and another angle measures 100^\circ

  2. A triangle has an angle measuring 90^\circ , an angle measuring 20^\circ , and a side that is 6 units long. The 6-unit side is in between the 90^\circ and 20^\circ angles.

    1. Sketch this triangle and label your sketch with the given measures.
    2. How many unique triangles can you draw like this?
    1. Find a value for x that makes \text-x less than 2x .
    2. Find a value for x that makes \text-x greater than 2x .

  4. One of the particles in atoms is called an electron. It has a charge of -1. Another particle in atoms is a proton. It has charge of +1.

    The overall charge of an atom is the sum of the charges of the electrons and the protons. Here is a list of common elements.

    charge from
    electrons    		 charge from
    protons    		 overall
    charge
    carbon -6 +6 0
    aluminum -10 +13
    phosphide -18 +15
    iodide -54 +53
    tin -50 +50

    Find the overall charge for the rest of the atoms on the list.

  5. A factory produces 3 bottles of sparkling water for every 7 bottles of plain water. If those are the only two products they produce, what percentage of their production is sparkling water? What percentage is plain?