### Key Concepts

- Identify angles created by parallel lines cut by a transversal
- Find unknown angle measures
- Use algebra to find unknown angle measures

**Lines Angles and Transversals**

- What is meant by similar figures?

- Which symbols is used to indicate similarity?

- What is the sequence of transformations for the image given?

**Answers:**

- Similar figures are two figures having the same shape. The objects which are of exactly the same shape and size are known as congruent objects.

- This symbol is used for similarity.

- Reflect over the x-axis, then translate (x+6, y)

**Angles, Lines and Transversals**

#### Angle:

Angles are formed when two lines intersect at a point.

#### Line:

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A transversal is a line that passes through two lines in the same plane at two distinct points.

**Transversal:**

**Identify Angles Created by Parallel Lines Cut by a Transversal**

#### Parallel lines:

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

#### Transversal:

When any two parallel lines are cut by a transversal, many pairs of angles are formed.

There is a relationship that exists between these pairs of angles.

While some of them are congruent, the others are supplementary.

**Example:**

#### Identify angles created by parallel lines cut by a transversal.

**Sol:**

**Parallel Lines Cut by a Transversal**

From the figure corresponding angles formed by the intersection of the transversal are:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

The pair of corresponding angles are equal in measure, that is,

∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8

**Alternate interior angles:**

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal. In the figure given above, there are two pairs of alternate interior angles.

∠3 and ∠6

∠4 and ∠5

The pair of alternate interior angles are equal in measure, that is, ∠3 = ∠6, and ∠4 = ∠5

**Alternate exterior angles:**

When two parallel lines are cut by a transversal, the pairs of angles formed on either side of the transversal are named as alternate exterior angles. From the figure given above, there are two pairs of alternate exterior angles.

∠1 and ∠8

∠2 and ∠7

The pair of alternate exterior angles are equal in measure, that is, ∠1 = ∠8, and ∠2 = ∠7

**Consecutive interior angles:**

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles. From the figure, there are two pairs of consecutive interior angles.

∠4 and ∠6

∠3 and ∠5

Unlike the other pairs given above, the pair of consecutive interior angles are supplementary, that is, ∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.

### Find Unknown Angle Measures

**Example:**

What is the measures of m ∠6? Explain.

**Sol:**

Use what you know about the angles created when parallel lines are cut by transversal.

m ∠6 + 59° = 180°

m ∠6 = 180° – 59°

m ∠6 = 121°

### Use Algebra to Find Unknown Angle Measures

**Algebra: **

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition (+), subtraction (-), multiplication (×), and division (/).

Below image is the example for algebraic expression.

**Example:**

In the figure given below, let the lines l_{1} and l_{2} be parallel and t is transversal. Find the value of x.

**Sol:**

From the given figure,

∠ (2x + 20) ° and ∠ (3x – 10) ° are corresponding angles.

So, they are equal.

Then, we have

(2x + 20) ° = (3x – 10)°

2x + 20 = 3x – 10

Subtract 2x from each side.

20 = x – 10

Add 10 to each side.

30 = x

**Exercise**

- Given the following two parallel lines that have been cut by a transversal. ∠1 and which angle make up alternate interior angles?

- Find the missing angle measures.

- Find the unknown angle.

- Find the value of x in the following figure.

- What type of angle pair is ∠1 and ∠3?

- Solve for x.

- Find x.

- Given the following two parallel lines that have been cut by a transversal.

Which two angles would be alternate exterior?

- For the given figure, can you conclude that r∥s? Explain.

- Solve for x.

### What we have learned:

- Understand Angles, Lines and Transversals
- Identify Angles Created by Parallel Lines Cut by a Transversal
- Find Unknown Angle Measures
- Use Algebra to Find Unknown Angle Measures

**Concept Map:**

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