Today we learned about
the angles in triangles and how they relate to each other.
Today’s objective: The
students will discover and apply the Interior Angle Sum Theorem and the
Exterior Angle Theorem for triangles.
Today’s TEKS: G.9.B - Formulate and test conjectures about the
properties and attributes of polygons and their component parts based on
explorations and concrete models.
First, we were each told to
draw a triangle. Then we learned
about using a protractor to measure the interior angles in the triangles. We all realized that the sum of the
interior angles in our triangles was 180 degrees, no matter what the triangle
looked like. This is known as the
Interior Angle Sum Theorem.
Interior Angle Sum
Theorem- The sum of the measures of the interior angles of a triangle is 180
degrees.
Next, we learned
that the angle formed by one side of triangle with the extension of another
side is called an exterior angle of the triangle. We all drew an exterior angle on our triangles and tried to
relate it to the interior angles.
We learned that the two angles that are not adjacent, or next to, the
exterior angle of the triangle are called remote interior angles. We discovered the exterior angle
theorem:
Exterior Angle Theorem-
The measure of the exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles.
I do have a question though. How many exterior angles does a triangle have? Is it three or six? If someone could answer in the comments, that would be great!
I think it's six. If you make all the line segments longer, then you get six angles next to the triangle, but you get nine angles altogether. Do the other three have a name, or do they just happen?
ReplyDeleteBut are there truly six since there are 3 pairs of equivalent angles? Yes you get 6 but is that considered the same angle? Mr Escalantes?
ReplyDeleteYea like Allie said those exterior angles are congruent because they are vertical angles, so I think there are just 3 pairs of congruent exterior angles.
ReplyDelete