Maryland Math 8.GR.A.3
The Standard
Use informal arguments to verify that the sum of the interior angles of a triangle is 180 degrees and why an exterior angle equals the sum of the two remote interior angles.
Maryland College and Career Ready Standards for Mathematics (2025) · MAKE CONJECTURES ABOUT AND VERIFY GEOMETRIC RELATIONSHIPS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain why the three angles of a triangle make a straight angle. They extend one side and explain why the outside angle equals the two nonadjacent inside angles added together.
What Mastery Looks Like
- A student can draw a line through a triangle's top vertex parallel to its base and use matching angles to show the total is 180 degrees. They can then use the straight angle beside an exterior angle to explain why it equals the other two inside angles added together.
Common Misconceptions
- Some students include the inside angle beside the exterior angle when adding the two angles. Others think measuring a few triangles proves the rule for every triangle.
How to Assess It
- Exit ticket: Draw a triangle and extend one side. Without measuring, use a parallel line or straight angles to explain both angle relationships.
Lesson moves
Ways to Teach It
Cut matching triangles, extend one side, line up one copy's torn corners, and fit its remote corners over the other's exterior angle.
Draw a line through a triangle's top vertex parallel to its base; explain which angles match and why they form a straight angle.
Give pairs triangle diagrams with an exterior angle marked; have them label the remote angles and write a two-step explanation using straight angles.
Trace a triangular roof truss from a photo, extend one beam, and show how the two distant inside angles make the outside angle.
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Printable 8.GR.A.3 Worksheet
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