Special Right Triangles, Nets, Complementary and Supplementary Angles, and Dilations.

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Presentation transcript:

Special Right Triangles, Nets, Complementary and Supplementary Angles, and Dilations

Special Right Triangles There are two special right triangles! We will use the Pythagorean Theorem to discover the relationships between the sides of the two special triangles.

Isosceles Right Triangle Conjecture or Rule In an isosceles right triangle, if the legs have length s, then the hypotenuse has length _______ Think: side – side – side

Lets try a few: Find the missing sides 1) 2) x x yy 52= x

The other special triangle is a If you fold an equilateral triangle along one of its altitudes you get a triangle. Therefore, a triangle is one half an equilateral triangle so it appears in math and engineering frequently as well Side across from 30 o is the shortest side, AIMS reference calls this side ____ Side across from 60 o is the medium side Side across from 90 o is the hypotenuse

Triangle Conjecture In a triangle, (easy as 1, 2, 3) if the shorter side has length s, (think 1s) then the hypotenuse has length _____and the longer leg has length ______ Think: side – side – 2 · side

x x y y 15 x 5. examples:

10 x x y 21 y x

Complement and Supplement A pair of has a sum of 90°. A pair of has a sum of 180° ° 70° A B 34 30° 150° C D complementary angles supplementary angles

Warm-Up: Dilations Where have you heard the word “dilate” before? What does it mean? To make wider or larger; cause to expand Eyes – more light, pupils get smaller

1. Dilations non-rigid SIMILAR Dilation: A non-rigid transformation in which the pre-image and the image are SIMILAR Dilations preserve angle measure, orientation, and collinearity Side length changes

Nets The two-dimensional representation of all the faces of a 3-dimensional figure What a 3-D figure would look like if you “unfold it”

Types of Nets Triangular Prism

Square Prism

Square Pyramid

Triangular Pyramid

Types of Triangles