Similar Polygons, Pythagorean Measurement Theorem ... Similar Poly… · Similar Polygons,...

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Name Date I can … Essential Question(s): Key Concepts Notes Similar Polygons Example 1 Determine whether the following figures are similar. Example 2 Given that the figures are similar, find the length of a missing side. Example 3Symone is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by 20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Symone determines that the width of the smaller box needs to be a minimum of 9 inches. What should be the minimum length of the box to hold the smaller mirror? *REMINDER-look at the similarity statement, figures may not be in correct order. Corresponding ANGLESCorresponding SIDESSimilar Polygons, Pythagorean Theorem, & Trigonometry part 1 Measurement

Transcript of Similar Polygons, Pythagorean Measurement Theorem ... Similar Poly… · Similar Polygons,...

Name Date I can … Essential Question(s):

Key Concepts Notes Similar Polygons – Example 1 – Determine whether the following figures are similar.

Example 2 – Given that the figures are similar, find the length of a missing side.

Example 3— Symone is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by 20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Symone determines that the width of the smaller box needs to be a minimum of 9 inches. What should be the minimum length of the box to hold the smaller mirror? *REMINDER-look at the similarity statement, figures may not be in correct order.

Corresponding ANGLES— Corresponding SIDES—

Similar Polygons, Pythagorean Theorem, & Trigonometry part 1 Measurement

Pythagorean Theorem Hypotenuse – Legs – Formula – Example 4 – Lati walks from her house 8 blocks directly north to her friend Dre’sha’s house, and then they walk 6 blocks directly east to the convenient store. If each block is exactly 200 feet, find the distance from Lati’s house to the store? (If she could walk a straight line from the store to her house) Hint: Draw a picture

Example 5 – Juwan plans to use a 25 foot ladder to paint his house. If he places the ladder so its base is 7 feet from the wall, how far up the wall is the top of the ladder? Example 6—Devon’s house is 10 miles east of the airport. When a jet has flown approximately 12 miles, it is directly above Devon’s house. Approximately how many miles high is the jet when it’s above his house?

Summary, Reflection, & Analysis

Exercise 1 Similar Polygons, Pythagorean Theorem, and Trigonometry

Name: ___________________________________ Date: _____________ SCORE: _______/30 pts

1. Jaylen and Ronald went on a camping trip. They parked their car and walked 1200 yards south, where they set

up their tent. Next they walked east for 900 yards looking for firewood. They begin walking north together, after

walking 500 yards; Jaylen stated that they are the same distance from the car as they are from the tent.

Determine whether Jaylen is correct. Show your work or explain your reasoning.

2. Find the value of x if ΔAEB ΔADC

3. If A is a right angle, then find the perimeter of ΔADC to the nearest tenth.

4. The polygons below are similar. Find the value of x and y.

5. If and are both perpendicular to , AC = 4 cm, AB = 2 cm, and EC = 8 cm, find ED.

6.

A graphic designer was given the sketch to create a similar computer drawing. The center line must be 10 cm long. Find

the values of x and y on the computer drawing.

Name Date I can … Essential Question(s):

Key Concepts Notes Trigonometry Sine Cosine Tangent Example 1 – Find the value of the given variable using trigonometric ratios.

a.

b. To find the angle measure, then you must use the ____________________.

Similar Polygons, Pythagorean Theorem, & Trigonometry part 2 Measurement

ANGLE of ELEVATION ANGLE of DEPRESSION Example 3—Antwanay is flying a kite. She drops the string holder 90 feet from a tree. The angle of elevation the string makes with the ground is 44°. Find the height of the tree and the length of the string.

Example 3—Similar trapezoids are shown below. Find the value of n.

Example 4—Chardenae’s house is 10 miles from the airport. The jet flew approximately 12 miles when it was directly above her house. What is the angle that the jet took off from the airport?

Summary, Reflection, & Analysis

Exercise 2 Similar Polygons, Pythagorean Theorem, & Trigonometry

Name: ___________________________________ Date: _____________ SCORE: _______/35 pts

1. The anchor wire of a telephone pole has snapped and needs to be replaced. The telephone pole is 30 feet tall.

The anchor for the wire is 13.8 feet from the bottom of the pole. What is the approximate length for the new

wire?

2. . If AC=10 and DF=20, find DE.

3. If is a right angle, find the measure of to the nearest tenth of a degree.

4. Using the figure to the right, find the height of the tree.

5. Using the figure to the right, find the angle of elevation.

6. Find all of the missing parts of the triangle (2 sides and 1 angle)

7.

Solve for x.