Question

for 25 - 29 answer with the correct statement.

• corresponding - alternate interior
• alternate exterior - consecutive

25 ∠3 and ∠6
26 ∠4 and ∠6
27 ∠2 and ∠7
28 ∠1 and ∠5
29 ∠1 and ∠8
diagram of intersecting lines with angles labeled 1,2,3,4,5,6,7,8
for 30 and 31 answer either with supplementary or congruent.
30 ∠4 and ∠6
31 ∠1 and ∠8
diagram of parallel lines cut by a transversal with angles labeled 1,2,3,4,5,6,7,8
for 32 - 33 find the slope that passes through the given points.

1. a(5,8) b(7,11)
2. c(0,7) d(4,8)

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates for problem 32

For points \( A(5, 8) \) and \( B(7, 11) \), we have \( x_1 = 5 \), \( y_1 = 8 \), \( x_2 = 7 \), \( y_2 = 11 \).

Step3: Calculate the slope for problem 32

Substitute into the slope formula: \( m=\frac{11 - 8}{7 - 5}=\frac{3}{2} \).

Step4: Identify the coordinates for problem 33

For points \( C(0, 7) \) and \( D(4, 8) \), we have \( x_1 = 0 \), \( y_1 = 7 \), \( x_2 = 4 \), \( y_2 = 8 \).

Step5: Calculate the slope for problem 33

Substitute into the slope formula: \( m=\frac{8 - 7}{4 - 0}=\frac{1}{4} \).

Answer:

1. The slope is \(\frac{3}{2}\)
2. The slope is \(\frac{1}{4}\)