Unit 1, Lesson 16
Drawing Triangles (Part 1)
Accelerated 7
16.1
Warm-up
Examine each set of triangles. What do you notice? What is the same about the triangles in the set? What is different?
Set 1:
Set 2:
16.2
Activity
Examine this set of triangles.
- What is the same about the triangles in the set? What is different?
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How many different triangles are there? Explain or show your reasoning.
Student Lesson Summary
Both of these quadrilaterals have a right angle and side lengths 4 and 5:
However, in one case, the right angle is between the two given side lengths, and in the other, it is not.
Two quadrilaterals each with two given side lengths labeled 4 and 5, and a right angle. On the left, the quadrilateral is a rectangle with the right angle between adjacent side lengths 4 and 5. On the right, the quadrilateral is a trapezoid with the bottom base labeled 5 and one leg labeled 4. There is a right angle between the bottom base and the leg not labeled.
If we create two triangles with three equal measures, but these measures are not next to each other in the same order, that usually means that the triangles are different.
Here is an example:
Two triangles. The triangle on the left has the angle labeled 32 degrees between the adjacent side lengths 5 and 6. The triangle on the right has the angle labeled 32 degrees between the side length labeled 5 and the third side of the triangle that is not labeled.
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 and :
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 and , there is only one way in which they can meet up and make a triangle:
Any triangle drawn with these three conditions will be identical to the one above, with the same side lengths and the same angle measures.
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