# Evelyn Arboleda

Geometry teacher | Verified Expert

I hold a degree in Geometry from Dakota State University. My passion lies in unraveling the intricacies of shapes and space, guiding students through the wonders of geometric concepts. With a knack for simplifying complex ideas, I foster a supportive learning environment where students thrive. Whether exploring angles, polygons, or proofs, I'm dedicated to illuminating the beauty and logic of Geometry. Let's embark on this geometric journey together!

## Questions

Two corners of an isosceles triangle are at #(5 ,2 )# and #(2 ,1 )#. If the triangle's area is #7 #, what are the lengths of the triangle's sides?

Points #(3 ,2 )# and #(8 ,1 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?

A parallelogram has an inscribed circle touching all its four sides. How do you prove that it is a rhombus?

Circle A has a center at #(3 ,2 )# and an area of #32 pi#. Circle B has a center at #(9 ,2 )# and an area of #24 pi#. Do the circles overlap?

Triangle A has sides of lengths #36 #, #42 #, and #48 #. 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?

Pg 24, q51. How do I figure this out? thanks

Explain how the formula for the area of a trapezoid is derived from the formula for the area of a triangle?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #21 #. What is the area of the triangle's incircle?

Is a rhombus a parallelogram?

Point P(−5, 2) is translated using the rule (x+3, y−1). What is the x-coordinate of P' ?

Triangle A has sides of lengths #24 #, #16 #, and #18 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?

A line segment is bisected by a line with the equation # 6 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?

One leg of a right triangle is 8 feet. The other leg is 6 feet. What is the length of the hypotenuse?

Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #48 #, how long are the other two sides?

If the ratio of the sides of two similar triangles is 4:9, how do you find the ratio of their areas?

The area of a rhombus is 65 square units. The length of one diagonal is 13 units. What is the length of the other diagonal?

What is the difference between a diamond and a rhombus?

Circle A has a center at #(5 ,3 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #16 pi#. Do the circles overlap? If not, what is the shortest distance between them?

A parallelogram has sides with lengths of #16 # and #5 #. If the parallelogram's area is #80 #, what is the length of its longest diagonal?

A line segment with endpoints at #(1 , -2 )# and #(1, -4 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?