Hotmath
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Title:
Hotmath
Author:
Hotmath
 

Problem: 1

are cut by the transversal . Classify the angles a and b .

 

Problem: 2

Use the given figure and name the pair of parallel lines and the transversal that form the given pair of angles.

2 and 3

 

Problem: 3

Classify the angle pairs with the same color labels.

 

Problem: 4

Sketch a large diagram showing three transversals intersecting two non parallel lines l and n . Number three pairs of same side interior angles on the same sides of the transversals, as in the given figure.

a) Calculate m 1 + m 2

b) Calculate m 3 + m 4

c) Calculate without measuring m 5 + m 6 and check the answer by measuring.

d) Write a conclusion.

 

Problem: 5

Justify the statement using a theorem or a postulate.

3 5

 

Problem: 6

Justify the statement using a theorem or a postulate.

7 8

 

Problem: 7

Identify a pair of parallel lines in the figure if 3 7. Justify your answer.

 

Problem: 8

Identify the parallel lines in the figure if 4 and 5 are supplementary angles. Justify your answer.

 

Problem: 9

Obtain the values of a and b .

 

Problem: 10

In the figure, m 2 = 60 , m 3 = 130 and

m 4 = (3 x – 9). If p || q , find x .

 

Problem: 11

The figure shows that x || y . Given that m p = 95 and m f = 42, find m b .

 

Problem: 12

Using the given figure and the information, name the segments that must be parallel. If there are no such segments, write none .

2 9

 

Problem: 13

Using the given figure and the information, name the segments that must be parallel. If there are no such segments, write none .

m 5 + m 6 = m 9 + m 10

 

Problem: 14

From the figure shown here, what are the values of a , b , and c ?

 

Problem: 15

In quadrilateral ABCD , m A = 67, m B = 43, m C = 137, m D = 113. Describe quadrilateral ABCD .

 

Problem: 16

Give the reasons to complete the proof: If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.

Given: Transversal s cuts lines p and q

2 1

Prove p || q

 

Problem: 17

The line containing the points ( x , 7) and (1, –1) is perpendicular to the line containing the points (3, 8) and (11, 2). What is the value of x ?

 

Problem: 18

A line passes through the points P (0, 10) and Q (4, 0). Determine its slope. Moving from left to right, state whether the line is vertical, horizontal, rising, or falling.

 

Problem: 19

A line passes through the points P (9, 2) and Q (–9, 2). Determine its slope. Moving from left to right, state whether the line is vertical, horizontal, rising, or falling.

 

Problem: 20

What value of y will make lines x and y parallel?

 

Problem: 21

What are the slopes of and given P (3, 3), Q (3, –1), R (1, 0), and S (–5, –3)? Also, determine whether and are perpendicular, parallel, or neither.

 

Problem: 22

What are the slopes of and given P (4, 1.5), Q (7, 3.5), R (1, –2), and S (3, –5)? Also, determine whether and are perpendicular, parallel, or neither.

 

Problem: 23

Use compass and straightedge. Draw a line and a point not on the line. Construct a second line through the point that is parallel to the first line, by duplicating alternate interior angles.

 

Problem: 24

Sketch the line y = 4, and plot the point A (–3, 6). Now, draw a perpendicular line segment from point A to the line. Calculate the distance between the point and the line.

 

Problem: 25

What is the distance between the two lines shown in the figure?