### Clarifications

*Clarification 1*: Postulates, relationships and theorems include measures of interior angles of a triangle sum to 180°; measures of a set of exterior angles of a triangle sum to 360°; triangle inequality theorem; 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.

*Clarification 2*: Instruction includes constructing two-column proofs, pictorial proofs, paragraph and narrative proofs, flow chart proofs or informal proofs.

*Clarification 3*: Instruction focuses on helping a student choose a method they can use reliably.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## MFAS Formative Assessments

Students are asked to explain why the sum of the lengths of the diagonals of an isosceles trapezoid is less than its perimeter.

Students are asked to prove that if a line intersecting two sides of a triangle divides those two sides proportionally, then that line is parallel to the third side.

Students are asked to prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Students are asked to explain why the sum of the measures of the interior angles of a convex *n*-gon is given by the formula (*n* – 2)180°.

Students are asked to prove that the base angles of an isosceles triangle are congruent.

Students are asked to provide an informal justification of the Triangle Sum Theorem.

Students are given a triangle in which the midpoints of two sides are shown and are asked to describe a method for locating the midpoint of the remaining side using only a straight edge and pencil.

Students are asked to prove that the medians of a triangle are concurrent.

Students are asked to describe a triangle whose vertices are the endpoints of a segment and a point on the perpendicular bisector of a segment.

Students are asked to prove the Triangle Inequality Theorem.

Students are asked to prove the Pythagorean Theorem using similar triangles.

Students are given the measure of one interior angle of an isosceles triangle and are asked to find the measure of another interior angle.

Students are given the lengths of two sides of a triangle and asked to describe all possible lengths of the remaining side.

Students are asked to prove that a line parallel to one side of a triangle divides the other two sides of the triangle proportionally.

Students are asked prove that the measures of the interior angles of a triangle sum to 180°.

Students are asked to explain why a quadrilateral formed by drawing the midsegments of a triangle is a parallelogram and to find the perimeter of the triangle formed by the midsegments.

## Original Student Tutorials Mathematics - Grades 9-12

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

## Student Resources

## Original Student Tutorial

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

Type: Original Student Tutorial