Name: _________________________
Date: __________________________
Use the diagram below for all problems in this section.
1. Name a pair of corresponding angles.
\(\angle 1 \& \angle 5\) (others possible)
2. Name a pair of alternate interior angles.
\(\angle 3 \& \angle 5\) or \(\angle 4 \& \angle 6\)
3. Name a pair of alternate exterior angles.
\(\angle 1 \& \angle 7\) or \(\angle 2 \& \angle 8\)
4. Name a pair of same-side interior angles.
\(\angle 4 \& \angle 5\) or \(\angle 3 \& \angle 6\)
5. Name an angle that forms a linear pair with \(\angle 2\).
\(\angle 1\) or \(\angle 3\)
6. Which angle corresponds to \(\angle 3\)?
\(\angle 7\)
7. Which angle is alternate exterior to \(\angle 2\)?
\(\angle 8\)
8. What is the name of the line 't' that intersects the other two lines?
Transversal
1. If \(m\angle 3 = 105^\circ\) and \(m\angle 5 = 105^\circ\), are lines l and m parallel? Why?
Yes, Converse of the Alt. Int. Angles Thm.
2. If \(m\angle 1 = 80^\circ\) and \(m\angle 5 = 80^\circ\), are lines l and m parallel? Why?
Yes, Converse of the Corresponding Angles Post.
3. If \(m\angle 4 = 70^\circ\) and \(m\angle 5 = 110^\circ\), are lines l and m parallel? Why?
Yes, Converse of the Same-Side Int. Angles Thm.
4. If \(m\angle 2 = 125^\circ\) and \(m\angle 8 = 125^\circ\), are lines l and m parallel? Why?
Yes, Converse of the Alt. Ext. Angles Thm.
5. Find x that makes l || m if \(m\angle 4 = (3x-10)^\circ\) and \(m\angle 8 = (2x+20)^\circ\).
\(3x-10 = 2x+20 \implies x=30\)
6. Find x that makes l || m if \(m\angle 4 = (2x+10)^\circ\) and \(m\angle 5 = (3x+20)^\circ\).
\((2x+10)+(3x+20)=180 \implies 5x=150 \implies x=30\)
7. Find x that makes l || m if \(m\angle 2 = (5x+5)^\circ\) and \(m\angle 8 = (6x-10)^\circ\).
\(5x+5 = 6x-10 \implies x=15\)
8. If \(m\angle 3 = 90^\circ\), what must \(m\angle 6\) be for the lines to be parallel?
\(90^\circ\)
For this section, assume lines l and m are parallel.
1. If \(m\angle 3 = 2x + 10\) and \(m\angle 5 = 3x - 5\), find x.
\(2x+10=3x-5 \implies x=15\)
2. If \(m\angle 4 = 4x + 20\) and \(m\angle 6 = 2x + 40\), find x.
\(4x+20=2x+40 \implies 2x=20 \implies x=10\)
3. If \(m\angle 1 = 5x - 25\) and \(m\angle 7 = 3x + 5\), find x.
\(5x-25=3x+5 \implies 2x=30 \implies x=15\)
4. If \(m\angle 3 = (x+25)^\circ\) and \(m\angle 6 = (2x-10)^\circ\), find \(m\angle 3\).
\(x+25+2x-10=180 \implies 3x=165 \implies x=55\). \(m\angle 3 = 80^\circ\)
5. If \(m\angle 5 = 75^\circ\), find \(m\angle 1\).
\(105^\circ\)
6. If \(m\angle 6 = 130^\circ\), find \(m\angle 8\).
\(50^\circ\)
7. If \(m\angle 1 = 3x + 40\) and \(m\angle 2 = 2x + 10\), find x.
\(3x+40+2x+10=180 \implies 5x=130 \implies x=26\)
8. If \(m\angle 5 = 4x\) and \(m\angle 8 = x + 20\), find \(m\angle 5\).
\(4x+x+20=180 \implies 5x=160 \implies x=32\). \(m\angle 5 = 128^\circ\)
Midpoint: \( M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) \)
Distance: \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \)
Use the diagram below as a visual aid for this section.
1. Find the midpoint of A(2, 5) and B(6, 9).
M(4, 7)
2. Find the midpoint of C(-3, 0) and D(5, -4).
M(1, -2)
3. Find the midpoint of E(7, -2) and F(-1, 6).
M(3, 2)
4. Find the midpoint of G(0, 8) and H(-10, 0).
M(-5, 4)
5. Find the distance between A(2, 5) and B(5, 9).
\(d = \sqrt{(5-2)^2 + (9-5)^2} = \sqrt{9+16} = \sqrt{25} = 5\)
6. Find the distance between C(1, 1) and D(6, 13).
\(d = \sqrt{(6-1)^2 + (13-1)^2} = \sqrt{25+144} = \sqrt{169} = 13\)
7. Find the distance between E(-2, 4) and F(3, -8).
\(d = \sqrt{(3-(-2))^2 + (-8-4)^2} = \sqrt{25+144} = \sqrt{169} = 13\)
8. Find the distance between G(0, 0) and H(-5, 12).
\(d = \sqrt{(-5-0)^2 + (12-0)^2} = \sqrt{25+144} = \sqrt{169} = 13\)