# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?

Is a rectangle a parallelogram always, sometimes or never?

A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

What is the orthocenter of a triangle with corners at #(3 ,3 )#, #(2 ,4 )#, and (7 ,9 )#?

What is the name of a polygon that has twice as many sides as a quadrilateral?

A line passes through #(8 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

A circle has a chord that goes from #( 5 pi)/6 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #20 pi #, what is the length of the chord?

A chord with a length of #16 # runs from #pi/4 # to #pi/2 # radians on a circle. What is the area of the circle?

A cone has a height of #5 cm# and its base has a radius of #5 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?

Triangle A has an area of #5 # and two sides of lengths #9 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #25 #. What are the maximum and minimum possible areas of triangle B?

Triangle A has an area of #12 # and two sides of lengths #3 # and #8 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?

A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(5 ,3 )#. How far is the triangle's centroid from the origin?

What is the area of a trapezoid whose diagonals are each 30 and whose height is 18?

A circle has a chord that goes from #pi/4 # to #pi/2 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?

The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1). Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not?

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #16 # and the triangle has an area of #112 #. What are the lengths of sides A and B?

An ellipsoid has radii with lengths of #8 #, #6 #, and #5 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

A triangle has two corners of angles #pi /6# and #(pi)/2 #. What are the complement and supplement of the third corner?

A line segment with endpoints at #(5 , -2 )# and #(2, -7 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

In a circle a diameter #AB# is drawn and on one side of it an arc #CD# is marked, which subtends an angle #50^@# at the center. #AC# and #BD# are joined and produced to meet at #E#. Find #/_CED#?