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  • Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =
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Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC = AC, then A, B, and C are collinear. If a + c = b + c, then a = b. If A and B are complementary, then mA + mB =90°. If A, B, and C are collinear, then AB + BC = AC.

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Page 1: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Warm UpState the converse of each statement.

1. If a = b, then a + c = b + c.

2. If mA + mB = 90°, then A and B are complementary.

3. If AB + BC = AC, then A, B, and C are collinear.

If a + c = b + c, then a = b.

If A and B are complementary, then mA + mB =90°.

If A, B, and C are collinear, then AB + BC = AC.

Page 2: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.

Page 3: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.

Example 1A:

m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30

m3 = 4(30) – 80 = 40 Substitute 30 for x.

m8 = 3(30) – 50 = 40 Substitute 30 for x.

ℓ || m Conv. of Corr. s Post.3 8 Def. of s.

m3 = m8 Trans. Prop. of Equality

Page 4: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.

Example 1B:

4 8

4 8 4 and 8 are corr. angles.

ℓ || m Conv. of Corr. s Post.

The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.

Page 5: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =
Page 6: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Example 2a

m4 = m8

Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.

4 8 4 and 8 are alternate exterior angles.

r || s Conv. of Alt. Int. s Thm.

4 8 Congruent angles

Page 7: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Example 2b

Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.

m3 = 2x, m7 = (x + 50), x = 50

m3 = 100 and m7 = 1003 7 r||s Conv. of the Alt. Int. s Thm.

m3 = 2x = 2(50) = 100° Substitute 50 for x.

m7 = x + 50 = 50 + 50 = 100° Substitute 5 for x.

Page 8: Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC =

Example 4

What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where y = 8. Show that the oars are parallel.

4y – 2 = 4(8) – 2 = 30° 3y + 6 = 3(8) + 6 = 30°

The angles are congruent, so the oars are || by the Conv. of the Corr. s Post.


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