Savannah Aguilar
Geometry teacher | Experienced educator in USA
I hold a degree in Geometry from Spring Hill College, where my passion for the intricacies of shapes and space flourished. With a commitment to fostering understanding and confidence in my students, I bring a dynamic approach to teaching. My goal is to make Geometry accessible and engaging, guiding learners through the maze of angles, proofs, and transformations with clarity and enthusiasm. Let's explore the wonders of geometry together, unlocking its mysteries one theorem at a time.
Questions
The diameter of a circle is 2 centimeters. What is the circle's radius?
A circle has a chord that goes from #( pi)/3 # to #(2 pi) / 3 # radians on the circle. If the area of the circle is #96 pi #, what is the length of the chord?
The volume of a cylinder is doubled without changing its height. How did its radius change?
A circle has a chord that goes from #( 3 pi)/4 # to #(15 pi) / 8 # radians on the circle. If the area of the circle is #54 pi #, what is the length of the chord?
A line passes through #(2 ,8 )# and #(4 ,9 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?
How do you find the area of a trapezoid with vertices (-7,1) (-4,4) (-4,-6) and (-7,-3)?
A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #28 #, what is the length of side BC?
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 #18 # and the height of the cylinder is #1 #. If the volume of the solid is #25 pi#, what is the area of the base of the cylinder?
A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?
Two corners of an isosceles triangle are at #(2 ,6 )# and #(4 ,8 )#. If the triangle's area is #48 #, what are the lengths of the triangle's sides?
How do you use Heron's formula to find the area of a triangle with sides of lengths #23 #, #21 #, and #20 #?
Point A is at #(9 ,3 )# and point B is at #(1 ,-6 )#. Point A is rotated #pi/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?
Points A and B are at #(4 ,5 )# and #(2 ,0 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?
A triangle has corners at #(-1 ,3 )#, #(3 ,-2 )#, and #(8 ,4 )#. If the triangle is dilated by a factor of #5 # about point #(-2 ,6 ), how far will its centroid move?
Two circles have the following equations: #(x +6 )^2+(y -1 )^2= 49 # and #(x +4 )^2+(y +7 )^2= 81 #. 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?
Point A is at #(2 ,-3 )# and point B is at #(6 ,-6 )#. Point A is rotated #pi # 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?
Circle A has a radius of #5 # and a center of #(2 ,7 )#. Circle B has a radius of #1 # and a center of #(3 ,1 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
How do you use Heron's formula to find the area of a triangle with sides of lengths #3 #, #5 #, and #4 #?
A triangle has corners at #(7 ,6 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?