GEOM.MATH.6.D
Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems.
Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
theoremtriangleproofPythagorean Theoreminterior anglesbase anglesisosceles trianglemidsegmentmedianrelationshipsproblems
Skills
- verify (theorems about relationships in triangles) #dok3
- prove (Pythagorean Theorem, sum of interior angles, base angles of isosceles triangles, midsegments, medians) #dok3
- apply (theorems about relationships in triangles to solve problems) #dok2
- explain (mathematical reasoning for triangle theorems) #dok3
Learning Targets
- I can identify relationships in triangles such as angle sums, midsegments, medians, and base angles. #dok1
- I can recall and state the Pythagorean Theorem and other triangle theorems. #dok1
- I can use triangle theorems to solve for missing side lengths or angles in triangles. #dok2
- I can apply theorems about triangles to solve real-world and mathematical problems. #dok2
- I can justify why the sum of the interior angles of a triangle is 180 degrees using a proof. #dok3
- I can prove the Pythagorean Theorem using deductive reasoning. #dok3
- I can verify the base angles of an isosceles triangle are congruent through proof. #dok3
- I can demonstrate how to find and use midsegments and medians in triangles using formal reasoning. #dok3
Big Ideas
- There are specific theorems about triangles, such as the Pythagorean Theorem and properties of medians and midsegments, that can be proven and used to solve problems.
- Proving and applying triangle relationships enhances the understanding and problem-solving ability in geometry.
Essential Questions
- How can proving theorems about triangles help us solve geometric problems?
- What relationships exist between the angles and sides of triangles?
- How can you justify that the sum of the interior angles of every triangle is always 180 degrees?
- What is the significance of the Pythagorean Theorem in geometry and real life?
- How do midsegments and medians contribute to our understanding of triangles?