### General Information

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

**Grade:**912

**Strand:**Geometric Reasoning

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

**Status:**State Board Approved

Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.

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

Course Number1111 |
Course Title222 |

1200400: | Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |

1206310: | Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |

1206320: | Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |

1206315: | Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |

7912065: | Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current)) |

Access Point Number |
Access Point Title |

MA.912.GR.1.AP.3 | Use the relationships and theorems about triangles. Solve mathematical and/or real-world problems involving postulates, relationships and theorems of triangles. |

Name |
Description |

The Measure of an Angle of a Triangle | Students are given the measure of one interior angle of an isosceles triangle and are asked to find the measure of another interior angle. |

Proving the Triangle Inequality Theorem | Students are asked to prove the Triangle Inequality Theorem. |

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

Triangles and Midpoints | 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. |

Interior Angles of a Polygon | Students are asked to explain why the sum of the measures of the interior angles of a convex |

The Third Side of a Triangle | Students are given the lengths of two sides of a triangle and asked to describe all possible lengths of the remaining side. |

Name That Triangle | 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. |

Locating the Missing Midpoint | 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. |

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

Geometric Mean Proof | 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. |

Converse of the Triangle Proportionality Theorem | 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. |

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

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

Median Concurrence Proof | Students are asked to prove that the medians of a triangle are concurrent. |

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

Isosceles Triangle Proof | Students are asked to prove that the base angles of an isosceles triangle are congruent. |

Name |
Description |

Triangles: Finding Interior Angle Measures | The lesson begins with a hands-on activity and then an experiment with a GeoGebra-based computer model to discover the Triangle Angle Sum Theorem. The students write and solve equations to find missing angle measures in a variety of examples. |

Right turn, Clyde! | Students will develop their knowledge of perpendicular bisectors & point of concurrency of a triangle, as well as construct perpendicular bisectors through real world problem solving with a map. |

Halfway to the Middle! | Students will develop their knowledge of mid-segments of a triangle, construct and provide lengths of mid-segments. |

Location, Location, Location, Location? | Students will use their knowledge of graphing concurrent segments in triangles to locate and identify which points of concurrency are associated by location with cities and counties within the Texas Triangle Mega-region. |

Name |
Description |

Proving Theorems About Triangles | 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. |

Name |
Description |

Proving Theorems About Triangles: | 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. |