Section R.3 Geometry Essentials.

Slides:

Advertisements

Similar presentations

Find the volume of a pyramid whose base is a square with sides of length L and whose height is h.

Advertisements

Laws of Sines and Cosines Sections 6.1 and 6.2. Objectives Apply the law of sines to determine the lengths of side and measures of angle of a triangle.

Exercise Solve x 2 = 4. x = ± 2. Solve x 2 = – 4. no real solution Exercise.

Special Right Triangles

Area of triangles Unit 5. Getting the idea  Area is a measure of the number of square units needed to cover a region.  Square Unit is a square with.

GOAL 1 PROPORTIONS IN RIGHT TRIANGLES EXAMPLE Similar Right Triangles THEOREM 9.1 If the altitude is drawn to the hypotenuse of a right triangle,

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.

EXAMPLE 1 Using a 45 o –45 o –90 o Triangle Softball The infield of a softball field is a square with a side length of 60 feet. A catcher throws the ball.

Geometry 11-3 Surface Areas of Pyramids and Cones.

11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.

Circles/Triangles Sector Area/ Arc Length Formulas Special Quads Polygons

= (2 in) · (2 in) = 4 in 2. P = a + b + c A = ½(8*8) A = 32 P = =20.

Geometry Section 9.4 Special Right Triangle Formulas

Aim: How do we find the lengths of the sides in a right triangle? Do Now 1. Solve 2(x + 5) = Find the measure of the missing angle? 48 o 17 o 100.

The Pythagorean Theorem

MA.912.G.5.1 : Apply the Pythagorean Theorem and its Converse. A.5 ft B.10 ft C. 15 ft D. 18 ft What is the value of x? x 25 ft 20 ft.

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

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

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 5 Polynomials and Factoring.

12.3 The Pythagorean Theorem

Apply the Pythagorean Theorem

Geometry Section 7.4 Special Right Triangles. 45°-45°-90° Triangle Formed by cutting a square in half. n n.

6-4 Circles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

1 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.

Involving right triangles

Scale drawings. Scale drawings are used when it is unrealistic to think about drawing an object in its actual size; so we need to “scale” them down Observe…

Warm Up 1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long. 2. The hypotenuse of a right triangle measures 17.

Sullivan Algebra and Trigonometry: Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

Let R be the region bounded by the curve y = e x/2, the y-axis and the line y = e. 1)Sketch the region R. Include points of intersection. 2) Find the.

*You will be able to find the lengths of sides of special right triangles And

Practice with Perimeter & Area

More Practice with the Trigonometric Functions Section 4.2b.

Section 1.7. Recall that perimeter is the distance around a figure, circumference is the distance around a circle, and area is the amount of surface covered.

Warm-Up Exercises 2. Solve x = 25. ANSWER 10, –10 ANSWER 4, –4 1. Solve x 2 = 100. ANSWER Simplify 20.

Jeopardy Pythag. Thm. Pythag. Thm. Apps Simplifying Radicals Inequalities Family Tree Of Numbers Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300.

EQ: What is the relationship between the 3 sides in a right triangle?

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Geometry.

6-4 Circles Warm Up Problem of the Day Lesson Presentation Pre-Algebra.

11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.

Objective - To find missing sides of right triangles using the Pythagorean Theorem. Applies to Right Triangles Only! hypotenuse c leg a b leg.

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Oak-Land Junior High Geometry Ch. 5 Presented by: Mrs. Haugan Math.

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.

SOLUTION Finding Perimeter and Area STEP 1 Find the perimeter and area of the triangle. Find the height of the triangle. Pythagorean Theorem Evaluate powers.

Section 8-1. Find the geometric mean between each pair of numbers. 4 and 9.

Objective The learner will solve problems using the Pythagorean Theorem.

Right Triangle Trigonometry A B C SOHCAHTOA. Geometry - earth measurement Trigonometry - triangle measurement Sine of an angle = Opposite leg Hypotenuse.

Chapter 7 Right Triangles and Trigonometry Objectives: Use calculator to find trigonometric ratios Solve for missing parts of right triangles.

10-2 The Pythagorean Theorem Hubarth Algebra. leg hypotenuse Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs.

Geometry Section 7.1 Apply the Pythagorean Theorem.

9.2; 11-13, 24-26, ~ ~

Pythagorean Theorem and Its Converse

Solving Applications 5.8 Applications The Pythagorean Theorem.

Area of a Rectangle = base x height

9.2 Special Right Triangles

11.2 Pythagorean Theorem.

The Pythagorean Theorem

8-1 Vocabulary Geometric mean.

Objective - To find missing sides of right triangles using the Pythagorean Theorem. Applies to Right Triangles Only! hypotenuse c leg a b leg.

6-3 The Pythagorean Theorem Pythagorean Theorem.

15.6 – Radical Equations and Problem Solving

Geometry Chapter 8 Review

Geometry Section

1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4

The Pythagorean Theorem

10-1 The Pythagorean Theorem

Right Triangles and Trigonometry

7-3 Special Right Triangles

Presentation transcript:

Section R.3 Geometry Essentials

OBJECTIVE 1

In a right triangle, one leg has a length 6 and the other has length 8 In a right triangle, one leg has a length 6 and the other has length 8. What is the length of the hypotenuse?

Show that a triangle whose sides are of lengths 5, 3, and 4 is a right triangle. Identify the hypotenuse.

Excluding antenna, the tallest inhabited building in the world is Taipei 101 in Taipei, Taiwan. If the indoor observation deck is 1437 feet above ground level, how far can a person standing on the observation deck see (with the aid of a telescope)? Use 3960 miles for the radius of Earth.

OBJECTIVE 2

A Christmas tree ornament is in the shape of a semicircle on top of a triangle. How many square centimeters of copper is required to make the ornament if the height of the triangle is 5 cm and the base is 3 cm?

OBJECTIVE 3