# Autumn Armstrong

Geometry teacher | Experienced educator in USA

I'm passionate about Geometry and hold a degree from Roanoke College. My journey in education has been shaped by a deep curiosity for shapes, patterns, and spatial relationships. With years of experience, I guide students through the intricacies of Geometry, making concepts clear and accessible. My goal is to instill a love for problem-solving and critical thinking in every student I teach. Let's explore the fascinating world of Geometry together!

## Questions

Two corners of an isosceles triangle are at #(9 ,6 )# and #(4 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

Proof of the shortest distance from a point to a plane formula?

A circle has a chord that goes from #( 2 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?

A triangle has two corners with angles of # pi / 6 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #12 #, what is the largest possible area of the triangle?

When are similar figures congruent?

A chord with a length of #1 # runs from #pi/4 # to #pi/2 # radians on a circle. What is the area of the circle?

Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #24 #, how long are the other two sides?

What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(4 ,4 )#, and (8 ,6 )#?

Triangle A has sides of lengths #36 #, #44 #, and #32 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

Triangle A has sides of lengths #35 #, #25 #, 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?

The legs of a right triangle are 4 cm and 7 cm long. To the nearest cm, how long is the hypotenuse?

A clear plastic prism has six faces, each of which is a parallelogram of side length 1 meter. A diagonal made of nylon filament line connecting two opposite vertices of the solid has a length of 4 meters. ls the solid a cube?

Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

Is it possible to find the area of a trapezoid when given the lengths of the four sides but without knowing which of the sides are parallel?

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

An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(1 ,4 )# to #(5 ,1 )# and the triangle's area is #15 #, what are the possible coordinates of the triangle's third corner?

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

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

How do you write an equation of a circle with center at (0,0), d=12?

Two corners of a triangle have angles of #(5 pi ) / 12 # and # ( pi ) / 8 #. If one side of the triangle has a length of #4 #, what is the longest possible perimeter of the triangle?