# 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

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 #7 #, #2 #, and #9 #, respectively. What is the rectangle's area?

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?

A triangle has two corners with angles of # (2 pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?

A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #16 #, what is the length of its longest diagonal?

Two corners of an isosceles triangle are at #(9 ,2 )# and #(1 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

A line segment has endpoints at #(4 ,0 )# and #(2 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Describe a sequence of transformations that transform the graph of f(x) into the graph of g(x)? #f(x)=x^2# and #g(x)=(x-4)^2+4#

A circle has a center that falls on the line #y = 3/8x +3 # and passes through # ( 1 ,4 )# and #(2 ,9 )#. What is the equation of the circle?

A triangle has corners at #(2 ,4 )#, #(8 ,6 )#, and #(7 ,9 )#. How far is the triangle's centroid from the origin?

Circle A has a center at #(2 ,3 )# and a radius of #5 #. Circle B has a center at #(3 ,8 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

How do I find the perimeter of the triangle with the vertices (-2,2), (0,4), (1,-4)?

Points #(6 ,2 )# and #(1 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?

If length and breadth of a rectangle is doubled, what happens to its perimeter?

The length of a rectangle is #x+2# and the width is #x-6#. What is the perimeter of this rectangle?

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

A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #42 #, what is the length of side BC?

How can a quadrilateral be classified?

Cups A and B are cone shaped and have heights of #27 cm# and #24 cm# and openings with radii of #7 cm# and #14 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Angles A and B are corresponding angles formed by two parallel lines cut by a transversal. If #m/_A = 4x# and #m/_B = 3x+7#, what is the value of #x#?