Lesson 5

Noah says, “I constructed 2 perpendicular bisectors of triangle \(ABC\). That means the point where they intersect is the circumcenter!” Andre responds, “No, we still need to check the third perpendicular bisector to make sure it intersects at the same point.”

Do you agree with either of them? Explain or show your reasoning.

Construct the circumcenter of each triangle. Then, based on the locations of the circumcenters, classify each triangle as acute, right, or obtuse.

triangle A

triangle B

Select all quadrilaterals that cannot be cyclic.

a square with side length \(\sqrt5\) units

a 2 inch by 4 inch rectangle

a rhombus with side length 5 centimeters and angle measures 20 degrees and 160 degrees

quadrilateral \(ABCD\) in which angle \(A\) is 62 degrees, angle \(B\) is 97 degrees, angle \(C\) is 118 degrees, and angle \(D\) is 83 degrees

quadrilateral \(WXYZ\) in which angle \(W\) is 45 degrees, angle \(X\) is 135 degrees, angle \(Y\) is 90 degrees, and angle \(Z\) is 90 degrees

A quadrilateral \(ABCD\) has the given angle measures. Select the set of measurements which could come from a cyclic quadrilateral.

angle \(A\) is 70\(^\circ\), angle \(B\) is 110\(^\circ\), angle \(C\) is 70\(^\circ\), and angle \(D\) is 110\(^\circ\)

angle \(A\) is 60\(^\circ\), angle \(B\) is 50\(^\circ\), angle \(C\) is 120\(^\circ\), and angle \(D\) is 130\(^\circ\)

angle \(A\) is 100\(^\circ\), angle \(B\) is 110\(^\circ\), angle \(C\) is 70\(^\circ\), and angle \(D\) is 80\(^\circ\)

angle \(A\) is 70\(^\circ\), angle \(B\) is 45\(^\circ\), angle \(C\) is 110\(^\circ\), and angle \(D\) is 45\(^\circ\)

What is the measure of angle \(YXZ\)?

A quadrilateral has vertices \(A=(0,0), B=(2,4), C=(0,5),\) and \(D=(\text-2,1)\). Select the most precise classification for quadrilateral \(ABCD\).

quadrilateral 

parallelogram 

rectangle

square