Chapter 9: Right Triangles and Trigonometry Lesson 9.1: Similar Right Triangles.

Slides:

Advertisements

Similar presentations

8-1 Similarity in Right Triangles

Advertisements

Geometric Mean Theorem I

9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.

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,

Altitudes Recall that an altitude is a segment drawn from a vertex that is perpendicular to the opposite of a triangle. Every triangle has three altitudes.

Assignment P. 361: 32, 34, 36 P : 1-3, 5-23, 30, 31, 33, 38, 39 Challenge Problems.

Geometric Mean & the Pythagorean Thm. Section 7-1 & 7-2.

MA.912.T.2.1 CHAPTER 9: RIGHT TRIANGLES AND TRIGONOMETRY.

Similar Right Triangles

7.4 Similarity in Right Triangles

9.1 Similar Right Triangles

Section 7.4 Similarity in Right Triangles. Geometric Mean The positive number of x such that ═

7.4 Similarity in Right Triangles In this lesson we will learn the relationship between different parts of a right triangle that has an altitude drawn.

10.1 Similar Right Triangles Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle,

Section 8-1 Similarity in Right Triangles. Geometric Mean If a, b, and x are positive numbers and Then x is the geometric mean. x and x are the means.

7-4 Similarity in Right Triangles

7.4 Similarity in Right Triangles

Section 9.1 Similar Right Triangles OBJECTIVE: To find and use relationships in similar right triangles BIG IDEAS: REASONING AND PROOF VISUALIZATIONPROPORTIONALITY.

Chapter 7.4.  The altitude is the Geometric Mean of the Segments of the Hypotenuse.

9.1 (old geometry book) Similar Triangles

Geometric Mean and Right Triangles

Right Triangles and Trigonometry Chapter Geometric Mean  Geometric mean: Ex: Find the geometric mean between 5 and 45 Ex: Find the geometric mean.

Warm Up Week 7. Section 9.1 Day 1 I will solve problems involving similar right triangles. Right Triangle – Altitude to Hypotenuse If the altitude.

Similar Right Triangle Theorems Theorem 8.17 – If the altitude is drawn to the hypotenuse if a right triangle, then the two triangles formed are similar.

Chapter 8 Lesson 4 Objective: To find and use relationships in similar right triangles.

Geometric Mean and the Pythagorean Theorem

To find the geometric mean between 2 numbers

Lesson 7-1 Geometric Means Theorem 7.1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two.

Use Similar Right Triangles

Similar Right triangles Section 8.1. Geometric Mean The geometric mean of two numbers a and b is the positive number such that a / x = x / b, or:

7.3 Use Similar Right Triangles

9.3 Similar Right Triangles. Do Now: Draw the altitude and describe what it is.

9.1 Similar Right Triangles Geometry. Objectives  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.

Section 8-1 Similarity in Right Triangles. Altitudes altitude Recall that an altitude is a segment drawn from a vertex such that it is perpendicular to.

Altitudes Recall that an altitude is a segment drawn from a vertex that is perpendicular to the opposite of a triangle. Every triangle has three altitudes.

7.4 Notes Similarity in Right Triangles. Warm-up:

Chapter 9: Right Triangles and Trigonometry Section 9.1: Similar Right Triangles.

Section 7-4 Similarity in Right Triangles. Hands-On Activity Take a piece of paper and cut out a right triangle. Use the edge of the paper for the right.

Geometry 6.4 Geometric Mean.

 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?

Find the geometric mean between: 1.6 and and 20 Geometric Mean x is the geometric mean between a and b. a x x b = Warm-up!!

Key Learning  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle.  Use a geometric mean.

9.1 Similar Right Triangles Geometry Mrs. Blanco.

8-1 Geometric Mean The student will be able to: 1.Find the geometric mean between two numbers. 2.Solve problems involving relationships between parts of.

9.1 Similar Right Triangles

Pythagorean Theorem and Special Right Triangles

9.1 Similar Right Triangles

Unit 3: Right Triangles and Trigonometry

Geometric Mean 7.1.

Right Triangles and Trigonometry

9.1 Similar Right Triangles

9.1 Similar Right Triangles

CHAPTER 8 Right Triangles.

Similar Right Triangles

X = 3 y = 6 r = 3 y = 20.

8-1: Similarity in Right Triangles

5.4: The Pythagorean Theorem

Chapter 7.3 Notes: Use Similar Right Triangles

7.3 Use Similar Right Triangles

Lesson 50 Geometric Mean.

Similar Right Triangles

5.4: The Pythagorean Theorem

9.1 Similar Right Triangles

Similarity in Right Triangles

8.1 Geometric Mean The geometric mean between two numbers is the positive square root of their product. Another way to look at it… The geometric mean is.

Using Similar Right Triangles

Similar Right Triangles

Right Triangles and Trigonometry

Similarity in Right Triangles

Presentation transcript:

Chapter 9: Right Triangles and Trigonometry Lesson 9.1: Similar Right Triangles

Theorems Thm 9.1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Theorems Thm 9.2: In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments

Theorems Thm 9.3: In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Example 1: A roof has a cross section that is a right triangle. T he diagram shows the approximate dimensions of this cross section m 14.6 m h 7.8 m a)Identify the similar triangles in the diagram b)Find the height, h, of the roof. a)  ABD ~  BCD ~  ACB b) 14.6h = h = 6.6 m A D C B

Example 2: Find the value of each variable x 610 a) X 2 = 60 x = y 5 8 Y 2 = 65 y = b)