Lesson 1
Lines, Angles, and Curves
- Let’s define some line segments and angles related to circles.
Problem 1
Find the values of \(x, y,\) and \(z\).
Problem 2
Give an example from the image of each kind of segment.
- a diameter
- a chord that is not a diameter
- a radius
Problem 3
Identify whether each statement must be true, could possibly be true, or definitely can’t be true.
- A diameter is a chord.
- A radius is a chord.
- A chord is a diameter.
- A central angle measures 90\(^\circ\).
Problem 4
Write an equation of the altitude from vertex \(A\).
Problem 5
Triangle \(ABC\) has vertices at \((5,0), (1,6),\) and \((9,3)\). What is the point of intersection of the triangle’s medians?
The medians do not intersect in a single point.
\((3,3)\)
\((5,3)\)
\((3,4.5)\)
Problem 6
Consider the parallelogram with vertices at \((0,0), (8,0), (4,6),\) and \((12,6)\). Where do the diagonals of this parallelogram intersect?
Problem 7
Lines \(\ell\) and \(p\) are parallel. Select all true statements.
Triangle \(ADB\) is congruent to triangle \(CEF\).
The slope of line \(\ell\) is equal to the slope of line \(p\).
Triangle \(ADB\) is similar to triangle \(CEF\).
\(\sin(A) = \sin(C)\)
\(\cos(B) = \sin(C)\)
Problem 8
Mai wrote a proof that triangle \(AED\) is congruent to triangle \(CEB\). Mai's proof is incomplete. How can Mai fix her proof?
We know side \(AE\) is congruent to side \(CE\) and angle \(A\) is congruent to angle \(C\). By the Angle-Side-Angle Triangle Congruence Theorem, triangle \(AED\) is congruent to triangle \(CEB\).
\(\angle A \cong \angle C, \overline{AE} \cong \overline{CE}\)
