Chapter 9 Angles & Pythagorean Theorem

Guiding Questions

How are they related?

Can I make a triangle?

What if it is a triangle?

What do I know about this triangle?

Chapter Outline:

9.1.1        Parallel Line Angle Pair Relationships

        WE WILL establish facts about angles formed when parallel lines are cut by a transversal.

        I WILL be able to determine angle measurement relationships given parallel lines cut by a transversal.

• R&P: 9-8 to 9-13 (9-8, 9-9, 9-13)

9.1.2        Finding Unknown Angles in Triangles

        WE WILL determine the sum of the angles in any triangle.

        I WILL be able to use this sum to solve for missing angles in triangles.

• R&P: 9-21 to 9-26 (9-21, 9-25, 9-26)

9.1.3        Exterior Angles of Triangles

        WE WILL define and implement the Exterior Angle Theorem.

        I WILL be able to use the Exterior Angle Theorem to solve for missing angles in triangles.

• R&P: 9-33 to 9-38 (9-34, 9-35, 9-38)

9.1.4        AA Triangle Similarity

        WE WILL investigate the AA Triangle Similarity.

        I WILL be able to use the AA Triangle Similarity to to solve for missing side lengths.

• R&P: 9-45 to 9-50 (9-46, 9-49, 9-50)

Summative Assessment: Section 9.1 Quiz

9.2.1        Side Lengths and Triangles

        WE WILL use cut-out squares to determine with combinations make triangles.

        I WILL be able to find and describe patterns in the combinations that make right, acute, and obtuse                 triangles.

• R&P: 9-56 to 9-67 (9-56, 9-58, 9-59, 9-61, 9-65, 9-67)

9.2.2        Pythagorean Theorem

WE WILL define and implement the Pythagorean Theorem.

        I WILL be able to use the Pythagorean Theorem to solve problems.

• R&P: 9-74 to 9-79 (9-74, 9-76, 9-78)

9.2.3        Understanding Square Root

        WE WILL discover various methods to estimate square root.

        I WILL be able to find square roots by estimation, by graphing, and by using a calculator.

• R&P: 9-88 to 9-99 (9-88, 9-90, 9-92, 9-93, 9-96, 9-98)

9.2.4        Real Numbers

        WE WILL distinguish rational and irrational numbers.

        I WILL be able to determine if a number is rational or irrational.

• R&P: 9-110 to 9-121 (9-110, 9-111, 9-112, 9-114, 9-115, 9-118)

9.2.5        Applications of the Pythagorean Theorem

        WE WILL solve various real-world problems using the Pythagorean Theorem.

        I WILL be able to effectively use the Pythagorean Theorem to solve these problems.

• R&P: 9-129 to 9-134 (9-129, 9-131, 9-133)

9.2.6        Pythagorean Theorem in Three-Dimensions

        WE WILL build a 3D model to look for right triangles in three dimensions.

        I WILL be able to effectively use the Pythagorean Theorem to solve these problems.

• R&P: 9-139 to 9-144 (9-139, 9-140, 9-142)

9.2.7        Pythagorean Theorem Proofs

        WE WILL explore two different proofs of the Pythagorean Theorem.

        I WILL be able to explain one of these two proofs in my own words.

• R&P: 9-149 to 9-154 (9-149, 9-151, 9-154)

Summative Assessment: Chapter 9 Test