Unit 7, Lesson 8
Triangles with 3 Common Measures
Grade 7
8.1
Warm-up
3 Sides; 3 Angles
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:
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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:
Examine this set of triangles.
How many different triangles are there? Explain or show your reasoning.
Examine this set of triangles.
How many different triangles are there? Explain or show your reasoning.
Both of these quadrilaterals have a right angle and side lengths 4 and 5:
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.
However, in one case, the right angle is between the two given side lengths, and in the other, it is not.
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.
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