Lesson 1 Menu 1.The triangles shown are similar. Find x and y. 2.Find the perimeter of ΔDEF if ΔABC ~ ΔDEF, AB = 6.3, DE = 15.75, and the perimeter of.

Slides:

Advertisements

Similar presentations

Lesson 5 Menu 1.Determine whether a regular quadrilateral tessellates the plane. Explain. 2.Determine whether a regular octagon tessellates the plane.

Advertisements

Find the area of the shaded region to the nearest tenth. Assume that

Triangle ABC is an isosceles triangle

Use the 45°-45°-90° Triangle Theorem to find the hypotenuse.

8.1: Geometric Mean Objectives: I will be able to….

1. Shown below is a Geometer’s Sketchpad screen

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,

The geometric mean can also be understood in terms of geometry. The geometric mean of two numbers, a and b, is the length of one side of a square whose.

Then/Now You have already found missing measures of similar triangles. (Lesson 6–7) Use the Pythagorean Theorem to find the length of a side of a right.

7.1 Geometric Mean.  Find the geometric mean between two numbers  Solve problems involving relationships between parts of right triangles and the altitude.

Lesson Menu Main Idea and New Vocabulary Key Concept:Pythagorean Theorem Example 1:Find a Missing Length Example 2:Find a Missing Length Key Concept:Converse.

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.

Similarity in Right Triangles Students will be able to find segment lengths in right triangles, and to apply similarity relationships in right triangles.

Over Lesson 11–1 A.A B.B C.C D.D 5-Minute Check 1 48 cm Find the perimeter of the figure. Round to the nearest tenth if necessary.

Find the perimeter and area of the parallelogram. Round to

Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches. Round to the nearest tenth. Find the.

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.

Proportions in Right Triangles Theorem 7.1 The altitude to the hypotenuse of a right triangle forms two triangles similar to it and each other.  ABC~

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 7) NGSSS Then/Now New Vocabulary Key Concept: Geometric Mean Example 1:Geometric Mean Theorem.

Honors Geometry Warm-up 1/30 Ashwin is watching the Super Bowl on a wide screen TV with dimensions 32” by 18” while Emily is watching it on an old square.

Warm Up Find the value of x. Leave your answer in simplest radical form. 7 x 9 x 7 9.

Lesson 4 Menu 1.Find the surface area of a cylinder with r = 10 and h = 6. Round to the nearest tenth. 2.Find the surface area of a cylinder with r = 4.5.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 11–4) NGSSS Then/Now Theorem 11.1: Areas of Similar Polygons Example 1: Find Areas of Similar.

Lesson 3 MI/Vocab composite figure Find the area of composite figures.

Find the surface area of the cone. Round to the nearest tenth.

SECTION 8.1 GEOMETRIC MEAN. When the means of a proportion are the same number, that number is called the geometric mean of the extremes. The geometric.

Geometric Mean CHAPTER 8.1. Geometric mean The geometric mean between two numbers is the positive square root of their product.

Geometric and Arithmetic Means

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 7) Then/Now New Vocabulary Key Concept: Geometric Mean Example 1:Geometric Mean Theorem 8.1.

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.

7.3 Use Similar Right Triangles

Lesson 5 Menu 1.Find the area of the figure. Round to the nearest tenth if necessary. 2.Find the area of the figure. Round to the nearest tenth if necessary.

9.2 Similar Polygons.

Lesson 3 Menu 1.The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger quadrilateral to the smaller quadrilateral.

Find the area of the figure. Round to the nearest tenth if necessary.

Then/Now You have already compared fractions and decimals. (Lesson 3–1) Identify and compare numbers in the real number system. Solve equations by finding.

Lesson 5 Menu 1.Find the surface area of the regular pyramid shown. Round to the nearest tenth if necessary. 2.Find the surface area of the regular pyramid.

Find the angle of elevation of the sun when a 6-meter flagpole casts a 17-meter shadow. After flying at an altitude of 575 meters, a helicopter starts.

Lesson 3 Menu 1.Find the lateral area of the prism shown. 2.Find the surface area of the prism shown. Round to the nearest tenth if necessary. 3.Find the.

Splash Screen. Concept When the means of a proportion are the same number, that number is called the geometric mean of the extremes. The geometric mean.

Lesson 2 Menu 1.Find the geometric mean between the numbers 9 and 13. State the answer to the nearest tenth. 2.Find the geometric mean between the numbers.

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

Lesson 7.3 Using Similar Right Triangles Students need scissors, rulers, and note cards. Today, we are going to… …use geometric mean to solve problems.

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.

Solve the proportion A. 15 B C. D Minute Check 1.

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

1. Are these triangles similar? If so, give the reason.

Distance Midpoint Distance Formula Pythagorean Theorem

Right Triangles and Trigonometry

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

Similar Right Triangles

Starter(s): Solve the proportion A. 15 B C. D. 18

8.1 Geometric Mean Objective: Find the geometric mean between two numbers, and solve problems involving right triangle and altitude relationships.

LESSON 8–1 Geometric Mean.

Chapter 7.3 Notes: Use Similar Right Triangles

Example 1: Solve a Right Triangle Example 2: Real-World Example

Lesson 50 Geometric Mean.

LESSON 8–1 Geometric Mean.

Similar 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.

Similar Right Triangles

Right Triangles with an altitude drawn.

Five-Minute Check (over Chapter 7) Mathematical Practices Then/Now

Presentation transcript:

Lesson 1 Menu 1.The triangles shown are similar. Find x and y. 2.Find the perimeter of ΔDEF if ΔABC ~ ΔDEF, AB = 6.3, DE = 15.75, and the perimeter of ΔABC is Refer to the figure. If MN = 5, NO = 3, and NP = 7, find MQ.

Lesson 1 MI/Vocab geometric mean Find the geometric mean between two numbers. Solve problems involving relationships between part of a right triangle and the altitude to its hypotenuse.

Lesson 1 KC1

Lesson 1 Ex1 Geometric Mean A. Find the geometric mean between 2 and 50. Answer: The geometric mean is 10. Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify.

Lesson 1 Ex1 Geometric Mean B. Find the geometric mean between 25 and 7. Answer: The geometric mean is about Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify. Use a calculator.

A.A B.B C.C D.D Lesson 1 CYP1 A.3.9 B.6 C.7.5 D.4.5 A. Find the geometric mean between 3 and 12.

A.A B.B C.C D.D Lesson 1 CYP1 A.12 B.4.9 C.40 D.8.9 B. Find the geometric mean between 4 and 20.

Lesson 1 TH1

Lesson 1 TH2

Lesson 1 Ex2 Altitude and Segments of the Hypotenuse In ABC, BD = 6 and AD = 27. Find CD. Δ

Lesson 1 Ex2 Answer: CD is about 12.7 Altitude and Segments of the Hypotenuse Cross products Take the positive square root of each side. Use a calculator.

Lesson 1 CYP2 1.A 2.B 3.C 4.D A.11 B.36 C.4.7 D.8.5 Find EG. Round your answer to the nearest tenth.

Lesson 1 Ex3 KITES Ms. Alspach is constructing a kite for her son. She has to arrange perpendicularly two support rods, the shorter of which is 27 inches long. If she has to place the short rod 7.25 inches from one end of the long rod in order to form two right triangles with the kite fabric, what is the length of the long rod?

Lesson 1 Ex3 Draw a diagram of one of the right triangles formed. Let be the altitude drawn from the right angle of ΔWYZ.

Lesson 1 Ex3 Answer: The length of the long rod is , or about 32.4 inches long. Cross products Divide each side by 7.25.

1.A 2.B 3.C 4.D Lesson 1 CYP3 A.68.3 ft B ft C ft D ft AIRPLANES A jetliner has a wingspan, BD, of 211 feet. The segment drawn from the front of the plane to the tail, at point E. If AE is 163 feet, what is the length of the aircraft to the nearest tenth of a foot?

Lesson 1 TH3

Lesson 1 Ex4 Find c and d in ΔJKL. Hypotenuse and Segment of Hypotenuse

Lesson 1 Ex4 Hypotenuse and Segment of Hypotenuse is the altitude of right triangle JKL. Use Theorem 8.2 to write a proportion. Cross products Divide each side by 5.

Lesson 1 Ex4 Answer: c = 20; d ≈ 11.2 Hypotenuse and Segment of Hypotenuse is the leg of right triangle JKL. Use the Theorem 8.3 to write a proportion. Cross products Take the square root. Simplify. Use a calculator.

A.A B.B C.C D.D Lesson 1 CYP4 A.13.9 B.24 C.17.9 D.11.3 A. Find e to the nearest tenth.

A.A B.B C.C D.D Lesson 1 CYP4 A.12.0 B.10.3 C.9.6 D.8.9 B. Find f to the nearest tenth.