# 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

How do you find the area of a isosceles triangle with base 10 and perimeter 36?

Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/12 # and the parallelogram's area is #14 #, how long are the other two sides?

A triangle has corners at points A, B, and C. Side AB has a length of #27 #. 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 #18 #, what is the length of side BC?

An ellipsoid has radii with lengths of #5 #, #12 #, and #7 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #12 #, #2 #, and #9 #, respectively. What is the rectangle's area?

Points A and B are at #(4 ,1 )# and #(3 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?

An ellipsoid has radii with lengths of #2 #, #2 #, and #3 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Two corners of an isosceles triangle are at #(2 ,9 )# and #(8 ,5 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

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

The following triangles are congruent by the SAS Congruence Postulate of Triangles?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

A line passes through #(2 ,8 )# and #( 7, 5 )#. A second line passes through #( 6, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

In a right triangle, is the side opposite the right angle the shortest side?

Point A is at #(1 ,-4 )# and point B is at #(-9 ,-8 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?

Consider a sector with angle #pi/3# radians, and radius #3.5 m#. What is the arc length and area?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(5pi)/8 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?

A triangle has corners at #(7 ,3 )#, #(9 ,4 )#, and #(5 ,2 )#. If the triangle is dilated by a factor of #2 # about point #(6 ,1 ), how far will its centroid move?

The hypotenuse is 6, and one of the leg is 4. How do you find the missing leg length?

A triangle has corners at points A, B, and C. Side AB has a length of #10 #. The distance between the intersection of point A's angle bisector with side BC and point B is #2 #. If side AC has a length of #8 #, what is the length of side BC?