Let's set it up and solve it  algebraically, letting x be the missing angle and see what we get:

Let's set it up and solve it  algebraically, letting x be the missing angle and see what we get:

Answer/Discussion to 3a
Figure ABCD is congruent to figure EFGH 
 

If B = 55, C = 45, and D = 30, what is the measure of G? 

Since G corresponds with C and the figures are congruent, then G = C = 45 degrees.
 
 

If AD = 10, EF = 15, and BC = 12, what is the length of EH?

Since side EH corresponds to side AD and the figures are congruent,
then side EH = side AD = 10.

(return to problem 3a)

If A = 30, C = 40, and E = 50, what is the measure of F? 

Since F corresponds to A and the figures are similar, then F = A = 30.
 

If AE = 10, FJ = 20, and BC = 40, what is the length of GH?

Since side GH corresponds to side BC and the figures are similar to each other, then GH and BC are in proportion to each other.  Similarly, FJ and AE are in proportion to each other.  When setting up the proportion, make sure that you set it up the same on both sides.

*Cross multiply
 
 
 
 

(return to problem 4a)

Find 2 if 7 = 50 degrees.

Since 2 and 7 are alternate exterior angles and the two lines are parallel, then 2  = 7 = 50 degrees.

(return to problem 5a)

Find 3 if 6 = 50 degrees.

Since 3 and 6 are alternate interior angles and the two lines are parallel, then 3 = 6 = 50 degrees.

(return to problem 5b)

Find 1 if 5 = 130 degrees.

Since 1 and 5 are corresponding angles and the two lines are parallel, then 1 = 5 = 130 degrees.

(return to problem 5c)

Find 4 if 6 = 50 degrees.

Since 4 and 6 are not alternate exterior, alternate interior or corresponding angles, they are not guaranteed to be equal. 

However, since 2 and 4 make a straight angle (180 degrees) and 2 and 6 are corresponding angles (which means they are equal), we can find the measure of 4.

4 = 130 degrees.

(return to problem 5d)