# 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

If #hatQ# is a Right-angle in #DeltaPQR and PR-PQ=9 , PR-QR=18# then what is the perimeter of the triangle?

A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #66 #, what is the length of its longest diagonal?

If the length of a rectangle is represented by #(5x-3)# and the width is represented by #(2x)#, what is the area of the rectangle in terms of #x#? Please show working.

A line segment is bisected by a line with the equation # - 5 y + 3 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?

A rectangle has three of its vertices at points #(3,4), # #(5,–4),# and #(–7, –7).# What is the #y# coordinate of the unknown vertex?

For which segment lengths is ¯¯¯AC¯ parallel to ¯¯DE¯ ?

A chord with a length of #13 # runs from #pi/8 # to #pi/2 # radians on a circle. What is the area of the circle?

Pre-image: A(−4, 2) , B(4, 4) , and C(−1, 2) Image: A′(−2, 1) , B′(2, 2) , and C′(−12, 1) Is the dilation an expansion or contraction? What is the scale factor?

A quadrilateral is a ______ if and only if its diagonals are perpendicular?

The angles of a triangle have the ratio 3:2:1. What is the measure of the smallest angle?

The base of a triangular pyramid is a triangle with corners at #(7 ,3 )#, #(4 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

A line segment with endpoints at #(-1, 1)# and #(3, -5)# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

What is the circumference of a circle with area = #36 pi# #cm^2#?

An ellipsoid has radii with lengths of #6 #, #7 #, and #6 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Point A is at #(8 ,-4 )# and point B is at #(-9 ,6 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

A circle has a center at #(7 ,5 )# and passes through #(4 ,3 )#. What is the length of an arc covering #pi /4 # radians on the circle?

What is the perimeter of a parallelogram with sides of 5 and 7?

Two circles have the following equations #(x +5 )^2+(y +6 )^2= 36 # and #(x +2 )^2+(y -1 )^2= 81 #. 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?

A conjecture and the flowchart proof used to prove the conjecture are shown. Match the expression or phrase to each box to complete the proof?

The radius of a pie measures 17 cm. What is the circumference of the pie?