# Ella Armstrong

Geometry teacher | Tutor for 7 years

I'm a passionate educator specializing in geometry. My journey began at Beloit College, where I delved deep into the intricacies of shapes, angles, and spatial relationships. With a keen eye for detail and a love for problem-solving, I aim to make geometry not just understandable but enjoyable for my students. Whether it's exploring the beauty of proofs or unraveling the mysteries of three-dimensional figures, I'm dedicated to fostering a supportive learning environment where students can thrive and develop their mathematical skills to their fullest potential.

## Questions

Can we say that all regular polygons are made from congruent isosceles triangles?

Points A and B are at #(4 ,9 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

Two corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 9 #, what is the longest possible perimeter of the triangle?

Circle A has a center at #(2 ,9 )# and an area of #16 pi#. Circle B has a center at #(3 ,8 )# and an area of #67 pi#. Do the circles overlap?

A line passes through #(9 ,3 )# and #( 3, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Points #(2 ,9 )# and #(1 ,5 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?

A triangle has corners at points A, B, and C. Side AB has a length of #24 #. 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 #35 #, what is the length of side BC?

What is the area of an equilateral triangle with a side length of 1?

A circle has a chord that goes from #( 4 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(pi)/2 #, and the triangle's area is #2 #. What is the area of the triangle's incircle?

Given two similar triangles with a scale factor of a : b, show the ratio of their perimeters is also a : b?

A rectangle with sides 7 and #x+2# has a perimeter of 40 units. What is the value of #x#?

A triangle has corners at #(-5 ,6 )#, #(2 ,-3 )#, and #(8 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,6 ), how far will its centroid move?

A line segment has endpoints at #(2 ,1 )# and #(6 ,2 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?

Two circles have the following equations #(x -1 )^2+(y -4 )^2= 64 # and #(x +3 )^2+(y +1 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

A square and a equilateral triangle are to be formed out of the same piece of wire. The wire is 6 inches long. What is the maximum of the total area the square and the triangle?

A rectangle has a perimeter of 48 ft. The length and width are scaled by a factor 1.5. What is the perimeter of the resulting rectangle?

What is the perimeter of a triangle with corners at #(7 ,5 )#, #(1 ,2 )#, and #(4 ,8 )#?

Triangle ABC is graphed on a coordinate plane. find the length of AB?

A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,5 )# and #(8 ,7 )#. What is the equation of the circle?