Download MAFS.912.G-CO.3.10: Prove theorems about triangles. Theorems i

Mathematics
Geometry
StandardMAFS.912.G-CO.3.10
Standard(s): MAFS.912.G-CO.3.10:
Prove theorems about triangles. Theorems include: measures
of interior angles of a triangle sum to 180°; 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.
Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning
Assessment Limits:
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Items may assess theorems and their converses for interior triangle sum, base angles of isosceles triangles,
mid-segment of a triangle, concurrency of medians, concurrency of angle bisectors, concurrency of
perpendicular bisectors, triangle inequality, and the Hinge Theorem.
Items may include narrative proofs, flow-chart proofs, two-column proofs, or informal proofs.
In items that require the student to justify, the student should not be required to recall from memory the
formal name of a theorem.
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The student will be able to:
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The student will be able to:
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Complete a proof for theorems about triangles with more than two steps.
Solve problems by applying algebra using the triangles inequality and the Hinge Theorems.
Solve problems by applying algebra for the Midsegment of a triangle.
Solve problems by applying algebra for the concurrency of angle bisectors.
Solve problems by applying algebra for the concurrency of perpendicular bisectors.
Complete proofs using the medians of a triangle that meet at the point called the centroid.
Prove theorems about triangles with no more than two steps in a proof that the measures of interior
angles of a triangle total 180°.
Prove theorems about triangles with no more than two steps in a proof that the base angles of an
isosceles triangle are congruent.
Probe theorems about triangles with no more than two steps in a proof that the segment joining
midpoints of two sides of a triangle (the Midsegment) is parallel to the third side of the triangle and
half the length of the third side.
Prove theorems about triangles with no more than two steps in a proof that the medians of a triangle
meet at a point inside the triangle called the centroid.
Solve problems about triangles using algebra.
Solve problems using the triangles inequality and the Hinge Theorem.
The student will be able to:
• Use theorems about interior angles of a triangle.
• Use theorems about exterior angles of a triangle.
• Completes proofs for theorems about triangles if the statements and reasons are both given as choices
and need to be reordered to create the proof.
Lastupdated8/11/16
Mathematics
Geometry
StandardMAFS.912.G-CO.3.10
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The student will be able to recognize the meaning of:
• Theorems, triangles, measures of interior angles of a triangle, base angles, isosceles triangle,
congruent, segment, midpoints, parallel, medians, midsegment, concurrent/concurrency, centroid,
Hinge theorem.
The student will be able to:
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Completes proofs for theorems about triangles if the statements are all given in order and the reasons
need to be selected from a list.
Identify the base angles in an isosceles triangle.
Identify midpoints on the sides of a triangle.
Identify a Midsegment of a triangle.
Lastupdated8/11/16