Ohhh what a Square! Developed by: Kenny Turnipseed Uwe Hoffmann.

Slides:

Advertisements

Similar presentations

Pythagoras Proofs TEKS 8.07 (C): The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.

Advertisements

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems using.

Using the Pythagorean Theorem in 3-Dimensional Shapes.

EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.

The Pythagorean Relationship

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

 Since the pythagorean relationship is true for all right triangles, we can write an algebraic equation to describe it: c² = a² + b² In the triangle.

Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares

Geometry Section 9.4 Special Right Triangle Formulas

Pythagorean Theorem step by step a c b Picture This!

Pythagorean Theorem. Right Triangle 90 degree angle Two short sides called legs One longer side called HYPOTENUSE.

Ch 11.3 – The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

Holt Course 2 NY-10 Using the Pythagorean Theorem NY-10 Using the Pythagorean Theorem Holt Course 2 Lesson Presentation Lesson Presentation.

Section 3-5 p. 137 Goal – to solve problems using the Pythagorean Theorem.

WARM UP Pass out progress reports! Get a Calendar from the front!

Special Right Triangles. Draw 5 squares with each side length increasing by

A b c. Pythagorean Theorem Essential Questions a 2 + b 2 = c 2 The Pythagorean Theorem a 2 + b 2 = c 2 “For any right triangle, the sum of the areas.

The Pythagorean Relationship. In words The Pythagorean Relationship states that in a right angle triangle, the square of the hypotenuse is equal to the.

Geometric and Arithmetic Means

Unit 6 - Right Triangles Radical sign aa Radicand Index b Simplifying Radicals 11/12/2015 Algebra Review.

Pythagorean Theorem Unit 7 Part 1. The Pythagorean Theorem The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Topic 10 – Lesson 9-1 and 9-2. Objectives Define and identify hypotenuse and leg in a right triangle Determine the length of one leg of a right triangle.

1. 2 Get a rectangular piece of paper and cut it diagonally as shown below. You will obtain two triangles with each triangle having half the area of the.

Lesson 11-3 Pages The Pythagorean Theorem.

 Rhombus – a parallelogram with four congruent sides.  Rectangle – a parallelogram with four right angles.

Special Right Triangles

The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

The Pythagorean Theorem a2 + b2 = c2

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares.

The Pythagorean Theorem The Ladder Problem. Right Triangles Longest side is the hypotenuse, side c (opposite the 90 o angle) The other two sides are the.

How can you prove the Pythagorean Theorem by using the diagram below?

Pythagorean Theorem & its Converse 8 th Grade Math Standards M.8.G.6- Explain a proof of the Pythagorean Theorem and its converse. M.8.G.7 - Apply the.

10-1 The Pythagorean Theorem. LEGS Hypotenuse Problem 1: Finding the Length of a Hypotenuse The tiles shown below are squares with 6-in. sides. What.

What is a right triangle? A triangle with a right angle.

Refresh Your Skills for Chapter 12.  If you split an equilateral triangle in half along an altitude, you create two right triangles with angles of 30°,

Success Criteria:  I can identify the pattern of special right triangles  I can put answers in standard radical form to identify patterns Today’s Agenda.

Geometry 7-2a Pythagorean Theorem. New Material Investigation Supplies –Handout ( one of two ) –Scissors –Compass –Ruler.

8-8 The Pythagorean Theorem Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Geometry 7-4 Area of Trapezoids, Rhombuses, and Kites.

WHAT IS THE PYTHAGOREAN THEOREM AND HOW DO WE USE IT TO ANALYZE RIGHT TRIANGLES? AGENDA: Simplifying radicals warmup Pythagorean theorem notes and practice.

 Lesson 7-4.  Draw one of the diagonals for your rectangle to form two right triangles. Q: What is the relationship between the two right triangles?

The Pythagorean Theorem

Pythagorean Theorem Geometry 7-2a.

Warm-Up Find x. 2x+12 =6 12x=24 √25 = x.

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems.

Pythagorean Theorem Geometry 7-2a.

The Pythagorean Theorem

9.3 The Converse of the Pythagorean Theorem

Lesson 11.4 Apply the Pythagorean Theorem and Its Converse

4.3 The Rectangle, Square and Rhombus The Rectangle

Measurement – Pythagorean Theorem

The Pythagorean Theorem a2 + b2 = c2

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

4.3 The Rectangle, Square and Rhombus The Rectangle

Drill: Tuesday, 1/13 For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form Simplify each expression

Trigonometry Math 10 Ms. Albarico.

Pythagorean Theorem a²+ b²=c².

The Pythagorean Theorem a2 + b2 = c2

Starter Work out the missing lengths for these squares and cuboids

(The Pythagorean Theorem)

The Pythagorean Theorem

Section 8.1 – 8.2 Geometric Mean Pythagorean Theorem

10-1 The Pythagorean Theorem

The Pythagorean Theorem a2 + b2 = c2

Presentation transcript:

Ohhh what a Square! Developed by: Kenny Turnipseed Uwe Hoffmann

Occupational Area: Construction CTE Concept: Framing a foundation. Math Concepts: Properties of Rectangles, Pythagorean Theorem

Lesson Objective: Students will be able to construct framework consisting of a four-sided shape with four right angles. Student will understand its application within the construction field and recognize its geometric relationship in other contexts. Supplies Needed: Tape Measure, String, Two 2”x4”x8’, Circular Saw, Hammer, Nails 1#16dup, Pencil, Cardboard, Scissors, Tape

1. Introduce the CTE Lesson We want to clarify the difference between being “a square” and being “in square”. I am going to show pictures of different shapes associated with the term square.

“A Square” vs. “In Square” a squarein square

“In Square” vs. “Not In Square” in squarenot in square

2. Assess Students’ Math Awareness as it relates to the CTE Lesson Knowing, that you are in a construction class, and after seeing the pictures, what might be the same and/or the difference by defining “a square” and “in square”? We will go ahead and use two 2”x4”x8’ and cut them in half. Lay out the pieces to construct a 3’x4’ frame. Cross tape the frame to assure it is “in square”.

3. Work through the Math Example embedded in the CTE Lesson Framework has four right angles, two equal diagonals, diagonals are part of a right triangle formed by two sides of the frame work, calculate the diagonal by applying the Pythagorean Theorem (PT). Draw a diagram of the framework, including the diagonals. Identify the right triangles within the diagram and label the sides.

4. Work through related, contextual Math-in-CTE Examples If the framework would be a window or a door, what would be the procedure to prove that they have right angles? Please draw a 2’0’x2’0 window frame. Calculate the diagonals to assure right angles. Please draw a 3’0’x6’8” doorframe. Calculate the diagonals to assure right angles

5. Work through traditional Math Examples. Assume the legs of a triangle are 6 in and 8 in. Find the length of the hypotenuse. A triangle has sides of 10 cm, 12cm, and 15 cm. Is the triangle a right triangle? Justify your answer.

6. Students demonstrate their Understanding Students use cardboard to construct and cut a rectangular cardboard framework. Explain the procedure and how to assure that the framework is “in square”. Use cardboard, scissors, and tape.

7. Formal Assessment Assessed by construction of class project. Written test covering geometric properties of rectangles, PT calculations, including structural drawing. Draw a sketch of an 8’ x 10’ patio. Label. Find the length of the diagonals to ensure “in square”.