Common Core: High School - Geometry : Construct Inscribed Figures (Equilateral Triangles, Squares, Regular Hexagons): CCSS.Math.Content.HSG-CO.D.13

Example Questions

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Example Question #21 : Construct Inscribed Figures (Equilateral Triangles, Squares, Regular Hexagons): Ccss.Math.Content.Hsg Co.D.13

Line  is perpendicular to line  where both lines are the diameter of the circle.  From this information triangle  must be a(n) _______ triangle.

right triangle

acute triangle

equilateral triangle

obtuse triangle

right triangle

Explanation:

Line  is perpendicular to line  and is 90 degrees.  We know this because line  intercepts an arc of 180 degrees.  An inscribed angle is half the measure of the intercepted arc. Therefore this must be a right triangle.

Example Question #22 : Construct Inscribed Figures (Equilateral Triangles, Squares, Regular Hexagons)

Find the side lengths of the square inscribed in the triangle.  The area of the entire triangle is 20.

Explanation:

Since we are finding the side lengths of a square, we really only need to find one side since all sides are congruent in a square.  Recall that the formula for the area of a triangle is .  We can find the area of the square by finding the area of the triangle and subtracting the area of the square.  Having the area of the square will just be one of the side lengths squared, so if we take the square root of the area of the square, we will have our answer.

First, consider the small triangle in the upper corner.  This is shown below:

The area of this triangle would be

We will consider the lower two triangles combined to be the second triangle:

The area of this triangle would be

And then we need to consider a third area which is the square

The area of the square would be

To get the total area of the triangle, we can sum all three areas.

We can sub in our areas and solve for to solve this problem

(multiply by 2 to get rid of fractions)

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