1 / 16

Warm Up

Warm Up. Find x. Leave answer as simplified radical. Special Right Triangles. 30 – 60 – 90 . Find the missing side lengths. 3 0º. Can we use Pythagorean Theorem? Can we use similar Triangles? Any other way we know of to find the missing side lengths?. 10. 60º. Before we begin….

gavin
Download Presentation

Warm Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Warm Up Find x. Leave answer as simplified radical

  2. Special Right Triangles 30 – 60 – 90

  3. Find the missing side lengths 30º • Can we use Pythagorean Theorem? • Can we use similar Triangles? • Any other way we know of to find the missing side lengths? 10 60º

  4. Before we begin… Lets go over some vocabulary needed

  5. Discovering Special Triangles • 1. Adam, a construction manager in a nearby town, needs to check the uniformity of Yield signs around the state and is checking the heights (altitudes) of the Yield signs in your locale. Adam knows that all yield signs have the shape of an equilateral triangle. Why is it sufficient for him to check just the heights (altitudes) of the signs to verify uniformity? • Because all equilateral triangles are similar so one measurement will be sufficient.

  6. Discovering Special Triangles • 2. A Yield sign from a street near your home is pictured to the right. It has the shape of an equilateral triangle with a side length of 2 feet. If the altitude of the triangular sign is drawn, you split the Yield sign in half vertically, creating two 30°-60°-90° right triangles, as shown to the right. For now, we’ll focus on the right triangle on the right side. (We could just as easily focus on the right triangle on the left; we just need to pick one.) We know that the hypotenuse is 2 ft., that information is given to us. The shorter leg has length 1 ft. Why?

  7. 2 2 2 2 2 2 1 1 Congruent due to HL So the two bottom legs must be congruent We know all sides have a length of 2. So if that side is split into 2 congruent pieces each piece must be 1.

  8. X 2 2 Pythagorean Theorem: 1 1 12 + x2 = 22 1 + x2 = 4 x2 = 3 x = 3.What is the length of the third side (the altitude)? Leave answer as simplified radical.

  9. Quick Review: How do we simplify radicals? 10 12 5 2 2 6 2 3 Break down the radicand (the number inside the radical) into perfect squares. Anything that is a perfect square will come out of the radical everything else stays inside the radical.

  10. Quick Review: How do you rationalize the denominator? = We can never leave a radical in the denominator. Multiply the numerator and denominator by the radical on the bottom. This will get rid of the radical on the denominator, then simplify.

  11. Answer question 4 on your own or in your pair

  12. 5) Now that we have found the altitudes of both equilateral triangles, we look for patterns in the data. Fill in the first two rows of the chart below, and write down any observations you make. Then fill in the third and fourth rows.

  13. 5) Now that we have found the altitudes of both equilateral triangles, we look for patterns in the data. Fill in the first two rows of the chart below, and write down any observations you make. Then fill in the third and fourth rows.

  14. 6. What is true about the lengths of the sides of any 30°-60°-90° right triangle? 30º 2x x 60º x

  15. Foldable!

  16. Once you have made your foldable complete the table for question 7

More Related