# Noah Atkinson

Geometry teacher | Tutor for 8 years

I am a dedicated educator specializing in Geometry, with a background in Mathematics from Washington and Lee University. My passion lies in guiding students through the intricate world of shapes, angles, and proofs, fostering their understanding and appreciation for the subject. With a commitment to clarity and patience, I strive to make geometric concepts accessible and engaging for learners of all levels. Through personalized instruction and effective problem-solving strategies, I aim to empower students to excel in their mathematical journey. Let's unlock the mysteries of Geometry together!

## Questions

A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #24 #, what is the length of side BC?

A triangle has two corners with angles of # ( pi ) / 2 # and # ( 5 pi )/ 12 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

A line passes through #(4 ,3 )# and #(2 ,6 )#. A second line passes through #(1 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Two corners of an isosceles triangle are at #(2 ,4 )# and #(4 ,7 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

A line segment goes from #(5 ,8 )# to #(4 ,2 )#. The line segment is reflected across #x=-3#, reflected across #y=-5#, and then dilated about #(2 ,0 )# by a factor of #2#. How far are the new endpoints from the origin?

Triangle A has an area of #6 # and two sides of lengths #9 # and #4 #. Triangle B is similar to triangle A and has a side with a length of #14 #. What are the maximum and minimum possible areas of triangle B?

Circle A has a center at #(3 ,5 )# and an area of #78 pi#. Circle B has a center at #(1 ,2 )# and an area of #54 pi#. Do the circles overlap?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #8 # and #9 # and the pyramid's height is #4 #. If one of the base's corners has an angle of #pi/3#, what is the pyramid's surface area?

A triangle has corners at #(2, 1 )#, #( 1, 3 )#, and #(5 , 5 )#. If the triangle is dilated by # 3 x# around #(1, 6)#, what will the new coordinates of its corners be?

What is the equation of the line that is perpendicular to the line #3x + y = 7# and passes through the point (6, -1)?

Two opposite sides of a parallelogram each have a length of #3 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #15 #, how long are the other two sides?

An equilateral triangle is an example of what kind of polygon? Convex, concave or irregular?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #9 # and the height of the cylinder is #6 #. If the volume of the solid is #135 pi#, what is the area of the base of the cylinder?

A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?

Two corners of an isosceles triangle are at #(4 ,2 )# and #(6 ,1 )#. If the triangle's area is #3 #, what are the lengths of the triangle's sides?

What is the perimeter of a triangle with corners at #(3 ,4 )#, #(2 ,7 )#, and #(4 ,5 )#?

How do you write an equation of a circle with center at (-8,8), d=16?

Triangle A has an area of #24 # and two sides of lengths #12 # and #6 #. Triangle B is similar to triangle A and has a side of length #9 #. What are the maximum and minimum possible areas of triangle B?

A triangle has corners A, B, and C located at #(3 ,5 )#, #(6 ,9 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

What are the applications of similar triangles in real life?