Geometry Unit 9

Big Idea:

Use the Pythagorean theorem, special right triangles and trigonometric ratios to find the missing sides of right triangles

Student Expectations:

Priority TEKS

G.9(A) [Readiness] determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

G.9(B) [Readiness] apply the relationships in special right triangles 30-60-90 and 45-45-90 and the Pythagorean theorem, including Pythagorean triples, to solve problems

Focus TEKS

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

G.8(B) [Supporting] identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems

Ongoing TEKS

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

Student Learning Targets:

• I will redraw and reorient similar triangles created when an altitude is drawn to the hypotenuse of a right triangle and solve problems.
• I will identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle.
• I will prove the right Triangle Altitude Theorem.
• I will use similar triangles to prove the Pythagorean Theorem.
• I will apply the Pythagorean Theorem and its converses to solve problems.
• I will develop and apply Pythagorean inequalities.
• I will describe and apply the relationships among the side lengths of 45-45-90 triangles.
• I will describe and apply the relationships among the side lengths of 30-60-90 triangles.
• I will find the ratios of side lengths in similar right triangles.
• Given an acute angle of a right triangle, I will identify the opposite leg and adjacent leg.
• I will calculate the trigonometric ratios in a right triangle.
• I will find side lengths and angle measures of right triangles using sine, cosine, and tangent in mathematical and real world context.
• I will use multiple methods to solve for missing sides of a right triangle when only one side is know.

Essential Questions:

• What alternatives are there for the Pythagorean Theorem when solving problems with right triangles?

Extra Information:

Adopted Textbook: Springboard - Geometry Texas Edition

District Grading Policy

Texas Gateway Online Resource Center