Wyoming Math G.CO.10

MathGrades 9–12Congruence

The Standard

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

2023 Wyoming Mathematics Content and Performance Standards · Prove geometric theorems.

Teacher's field guide

What This Standard Means

What Students Need to Do: Students use diagrams and known facts about angles, congruence, and parallel lines to write triangle proofs. They justify each step instead of measuring a drawing and calling it proof.
What Mastery Looks Like: Students can prove claims about a triangle's angle sum, equal base angles, and the segment connecting two side midpoints. They can also show why all three medians pass through one point.
Common Misconceptions: Students may treat a drawing or ruler measurement as proof. Some think the segment connecting two side midpoints is as long as the third side, or that the medians meet halfway along each median.
How to Assess It: Draw triangle ABC with D and E at the midpoints of AB and AC. Ask students to prove that DE is parallel to BC and half its length, with a reason for each step.

Lesson moves

Ways to Teach It

Fold a paper triangle to mark two side midpoints, connect them, compare lengths, then explain why the new segment is parallel to the base.
Ask pairs to draw an isosceles triangle and explain why a line from its top vertex to the base midpoint proves equal base angles.
Give pairs shuffled proof cards for the triangle angle sum; have them order the parallel-line and straight-angle steps and defend each move.
Give a roof-truss sketch with a 16-foot base; students mark midpoints on the sloped sides and justify an 8-foot parallel brace.

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