# Sadie Adams

Geometry teacher | Verified Expert

Greetings! I'm a dedicated geometry expert, honing my skills at Loyola University Maryland. Passionate about shaping mathematical minds, I thrive on unraveling the complexities of geometry. With a commitment to fostering understanding, I'm here to guide students through the intricacies of shapes, angles, and the beauty of mathematical relationships. Let's embark on a journey of geometric exploration together!

## Questions

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

A triangle has corners at #(9 ,3 )#, #(2 ,5 )#, and #(3 ,4 )#. How far is the triangle's centroid from the origin?

An interior angle of a parallelogram is 24 degree greater than double of the measure of the exterior angle adjacent to it.Determine the measure of the interior angle?

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

A line segment with endpoints at #(2 , 2 )# and #(5, -3 )# is rotated clockwise by #pi #. What are the new endpoints of the line segment?

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

Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/3 #, what is the difference between the areas of the rhombuses?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #8 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?

A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #49 #, what is the length of its longest diagonal?

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 #8 #. If side AC has a length of #18 #, what is the length of side BC?

A cube and a regular octahedron are carved out of of unit-radius wooden spheres . If the vertices are on the spheres, how do you prove that their volumes compare with that of the sphere, in the proportions #3/sqrt 2 : 2 : pi?#

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

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

If two supplementary angles have equal measures, what is the measure of each angle?

A triangle has two corners of angles #(3pi )/8# and #(pi)/4 #. What are the complement and supplement of the third corner?

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

An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is # 4 #, the cap's height is #2 #, and the cap's radius is #1 #. What is the object's volume?

What is the equation of the circle with a center at #(-1 ,2 )# and a radius of #7 #?

A line segment has endpoints at #(5 ,3 )# and #(5 ,4)#. If the line segment is rotated about the origin by #pi /2 #, translated horizontally by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Triangle A has an area of #9 # and two sides of lengths #4 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the maximum and minimum possible areas of triangle B?