Standard #: MA.912.GR.1.3


This document was generated on CPALMS - www.cpalms.org



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


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.



Related Courses

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))


Related Access Points

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.


Related Resources

Formative Assessments

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 n-gon is given by the formula (n – 2)180°.

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.

Lesson Plans

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.

Original Student Tutorial

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. 

Student Resources

Original Student Tutorial

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. 



Printed On:11/29/2022 6:56:25 AM
Print Page | Close this window