Geometry Unit 6

Big Idea:

Use the median, altitude and perpendicular bisectors to examine triangle properties and prove triangles congruent

Student Expectations:

Priority TEKS

G.6(B) [Readiness] prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions

Focus TEKS

G.5(A) [Readiness] investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

G.5(B) [Supporting] construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

G.5(C) [Supporting] use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships

G.5(D) [Supporting] verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems

G.6(D) [Supporting] 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

Ongoing TEKS

G.5(A) [Readiness] investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

G.6(C) [Supporting] apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles

Student Learning Targets:

• I will solve problems for missing sides or angles using the principles of congruence.
• I will develop criteria for proving triangle congruence.
• I will determine which congruence criteria can be used to show that two triangles are congruent
• I will write a proof in various formats (two-column and flowchart) and analyze why each is valid\
• I will convert two-column into flowchart proofs.
• I will write proofs using the fact that corresponding parts of congruent triangle are congruent. Prove and apply theorems about angle measures in triangles.
• I will develop and prove theorems about isosceles triangles.
• I will determine the point of concurrency of the altitudes, medians, and perpendicular bisectors of a triangle.
• I will use the point of concurrency of the altitudes, medians, and perpendicular bisectors of a triangle to solve

Essential Questions:

• How does deductive reasoning help me measure the validity of mathematical statements?
• Why is Angle-Angle-Angle or Side-Side-Angle insufficient to prove congruence of triangles?
• How do the characteristics of triangles provide the basis for understanding geometry?
• What determines the locations of the points of concurrency between special segments in a triangle?

Extra Information:

Adopted Textbook: Springboard - Geometry Texas Edition

District Grading Policy

Texas Gateway Online Resource Center