Sophia Alfred
Geometry teacher | Experienced educator in USA
I'm a Geometry expert, graduating from Shepherd University. My passion lies in unlocking the mysteries of shapes and spaces. With a knack for simplifying complex concepts, I empower students to conquer geometric challenges with confidence. Let's navigate the world of angles and proofs together!
Questions
Two angles are congruent and complementary. What is the measure of each angle?
Triangle A has sides of lengths #51 #, #45 #, and #54 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?
Two opposite sides of a parallelogram each have a length of #32 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #140 #, how long are the other two sides?
Two circles have the following equations #(x +5 )^2+(y +3 )^2= 9 # and #(x +4 )^2+(y -1 )^2= 1 #. 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?
The base of a triangular pyramid is a triangle with corners at #(3 ,1 )#, #(4 ,9 )#, and #(5 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
An ellipsoid has radii with lengths of #3 #, #6 #, and #5 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
What are the coordinates of the image of the point #(–3, 6)# after a dilation with a center of #(0, 0)# and scale factor of #1/3#?
I am a polygon, I have five sides that equal the same, and five angles that measure the same. What am I?
A triangle has corners A, B, and C located at #(5 ,6 )#, #(3 ,5 )#, and #(1 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #pi/3 #, what is the area of the parallelogram?
A parallelogram has sides with lengths of #12 # and #4 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?
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 #24 #, what is the length of side BC?
Triangle A has sides of lengths #15 #, #12 #, and #12 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?
What is the formula to find out the area of irregular pentagon?
Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?
A cone has a height of #32 cm# and its base has a radius of #9 cm#. If the cone is horizontally cut into two segments #12 cm# from the base, what would the surface area of the bottom segment be?
What is the area of an equilateral triangle whose perimeter is 48 inches?
A triangle has two corners with angles of # (2 pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?
Given the 2 sets of figures below, are the pairs of triangles similar for both set a and set b? Why or why not? What is the similarity statement and the scale factor?
What is the formula for finding the sum of all exterior angles?