7-3 Special Right Triangles

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Presentation transcript:

7-3 Special Right Triangles Honors Geometry April 8, 2013

Warm Up State if the triangle is acute, right or obtuse Is it possible to have an isosceles right triangle?

This week Quiz Tuesday! Pythagorean Theorem; Acute vs. Right vs. Obtuse Triangles; 45-45-90 Triangles; 30-60-90 Triangles; Simplifying Radicals Vocab Quiz Thursday! Vocab List was given out before spring break! On my website! Test Friday!

Agenda Warm Up Discovery Activity – Special Right Triangles 7-3 Special Right Triangles Notes Examples Homework

Discovery Activity Complete in your groups As a group, read through the worksheet and answer all questions You will be using your prior knowledge to answer questions and discover patterns Always attempt to do the problems and try new things with your group before asking for assistance When you are finished, have 1 student in your group report your findings to Ms. Wilson

7-3 Special Right Triangles 45-45-90 If the measures of the angles of a triangle are 45, 45, and 90, then the triangle is an isosceles right triangle

45-45-90 Triangle What pattern did you notice while working with 45-45-90 Triangles? The legs of a 45-45-90 Triangle are congruent the hypotenuse is times as long as a leg

Example 1 Find the value of x and y y=12, x=12sqrt(2)

Example 2 Find the value of x and y Label sides, n n and n rt 2, solve for n

30-60-90 Triangles In a 30-60-90 Triangle we have a short leg, long leg, and hypotenuse Hypotenuse Long Leg Short Leg

30-60-90 Triangles How can we find the lengths of the sides of a 30-60-90 Triangle? If we use reflection, what type of triangle do we have? Equilateral The value of m must be…? 2 Now we can work backwards to find n n= Extend to an equilateral triangle, which means all sides are now 2. Can now work backwards to find altitude

30-60-90 Triangles What pattern do we have with 30-60-90 Triangles? In a 30o-60o-90o Triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg

Example 3 Find the value of x and y

Example 4 Find the value of x and y Label sides!

Classwork Complete Evens or Odds from worksheet

Homework Complete worksheet