Even ANSWERS TO HOMEWORK

Slides:

Advertisements

Similar presentations

Things to do: ♥Make a new note book ♥Get out your homework (triangle worksheet)

Advertisements

Lesson 9-5 Pages The Pythagorean Theorem Lesson Check 9-4.

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.

TODAY IN GEOMETRY… Warm Up: Simplifying Radicals

EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.

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.

The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

Lesson 56: Special Right Triangles

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

Geometry Section 9.4 Special Right Triangle Formulas

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.

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.

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

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

Special Right Triangles Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

Do Now 5/16/11 Copy HW in your planner. Copy HW in your planner. Text p. 467, #8-30 evens, & 19 Text p. 467, #8-30 evens, & 19 Be ready to copy POTW #6.

Lesson Handout #1-49 (ODD). Special Right Triangles and Trigonometric Ratios Objective To understand the Pythagorean Theorem, discover relationships.

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

Working with square roots warm up 1.√3 + √3 = 2.√4 +√4 = 3.√5 + √5 = 4.√1 + √1 = 5.(√3) (√3) = 6.(√5) (√6) = Simplify 7. √24 = 8.√18 = 9.√81 = 10.√150.

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

Lesson 9.4 Geometry’s Most Elegant Theorem Objective: After studying this section, you will be able to use the Pythagorean Theorem and its converse.

This is a right triangle: We call it a right triangle because it contains a right angle.

- Special Right Triangles Chapter 4 Understanding Trigonometric Functions Language Objectives: We will review Special Right Triangles by do worksheet 11A.

11/27/ : Special Right Triangles1 G1.2.4: Prove and use the relationships among the side lengths and the angles of 30°- 60°- 90° triangles and 45°-

7.4.1 SPECIAL RIGHT TRIANGLES Chapter 7: Right Triangles and Trigonometry.

The Pythagorean Theorem

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

4.7 – Square Roots and The Pythagorean Theorem Day 2.

Rhombus. Properties of a Rhombus: A B C D All properties of a parallelogram All sides are congruent (equilateral) The diagonals are perpendicular The.

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

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

 Remember the pattern for right triangles: Area of small square + Area of medium square = Area of large square.

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.

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

Bellwork: ACT Review: Two sides of a triangle measure 6 and 15, what are the possible values for the measure of the third side of the triangle? Geometry.

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°,

– Use Trig with Right Triangles Unit IV Day 2.

Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form Simplify expression. 3.

Geometry Section 7.1 Apply the Pythagorean Theorem.

Special Right Triangles

Geometry/Trig 2 Name __________________________

8-1 Pythagorean Theorem and the Converse

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

Two Special Right Triangles

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

The Distance and Midpoint Formulas

SOL 8.10 Pythagorean Theorem.

Standard: MG 3.3 Objective: Find the missing side of a right triangle.

12-2 The Pythagorean Theorem

7.1 Apply the Pythagorean Theorem

a2 + b2 = c2 Pythagorean Theorem c c b b a a

6-3 The Pythagorean Theorem Pythagorean Theorem.

The Pythagorean Theorem

right triangles Some right triangles are used so frequently that it is helpful to remember some of their properties. These triangles are called.

9.2 A diagonal of a square divides it into two congruent isosceles right triangles. Since the base angles of an isosceles triangle are congruent, the measure.

6.5 Pythagorean Theorem.

(The Pythagorean Theorem)

Solve for the unknown side or angle x

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

GEOMETRY’S MOST ELEGANT THEOREM Pythagorean Theorem

5-3 Unit 5 Trigonometry.

Warm-up Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. a = b = a = 2.

The Pythagorean Theorem

9.4 Special Right Triangles

10-1 The Pythagorean Theorem

Presentation transcript:

Even ANSWERS TO HOMEWORK 28) 15/2 or 7.5 30) 13/6 or 2.167 32) x = 3√7, y = 12, z = 4√7 34) x = 8, y = 8√2, z = 8√2 36) x = 18, y = 12√2, z = 4√2

8-2 Pythagorean Theorem

PYTHAGOREAN THEOREM c b a c a b What side is ALWAYS the c? The HYPOTENUSE!! (Remember it’s across from the 90.) a b a and b are the legs. They can go in any order.

Example—Find c. c 6 8 62 + 82 = c2 36 + 64 = c2 100 = c2 C= 10

Problems 10 7 x2 + 49 = 100 x x 6 6 9

Isosceles Triangles Altitude of an isosceles triangle is also the median x x 2 2 4

Word problems Find the length of the diagonal of a square with perimeter 24. Draw a Picture always!!! How long is each side? (24/4=6) Make a triangle and solve the rest. Answer: Who got it??

Homework Page 292 #1-27 ODDS