Two parallel lines. Draw two parallel lines

### 1.1. Two parallel lines

- Extending the two sides AB and DC of the rectangle ABCD we get
*Two parallel lines*together. - Two parallel lines never intersect.

### 1.2. Draw two parallel lines

*Draw the line CD passing through the point E and parallel to the given line AB.*

We can draw like this:

- Draw the line MN passing through the point E and perpendicular to the line AB.
- Draw the line CD through the point E and perpendicular to the line MN, we get the line CD parallel to the line AB.

### 1.3. Textbook exercise solution page 51

**Lesson 1:**

a) Let ABCD, AB and DC be a parallel pair.

Name each pair of parallel sides in the rectangle.

b) Name each pair of parallel sides in the square MNPQ.

**Solution guide:**

- Observe the drawing to determine if the sides are parallel.

a) In rectangle ABCD there are:

AB and DC are pairs of parallel sides.

AD and BC are pairs of parallel sides.

b) In the square MNPQ there are:

– MN and PQ are pairs of parallel sides.

– MQ and NP are pairs of parallel sides.

**Lesson 2: **In the figure below, indicate that the quadrilaterals ABEG, ACDG, BCDE are all rectangles. Which sides are parallel to edge BE?

__Solution guide:__

- Observe the figure to determine if the sides are parallel.

BE is parallel to edge AG and edge CD.

**Lesson 3: **In each picture below

a) Name pairs of parallel sides;

b) Name pairs of sides that are perpendicular to each other.

__Solution guide:__

- Observe the drawing to determine if the sides are parallel.
- Observe the drawing to find pairs of sides that are perpendicular to each other, then you can check again with eke.

+) In the figure MNPQ there are:

a) MN is parallel to QP.

b) MN is perpendicular to MQ; QM is perpendicular to QP.

+) In the figure DEGHI there are:

a) DI is parallel to GH.

b) DE is perpendicular to EG; DI is perpendicular to IH; IH is perpendicular to GH.

### 1.4. Solve textbook exercises pages 53, 54

**Lesson 1: **Draw the line AB passing through the point M and parallel to the line CD .

__Solution guide:__

We can draw like this:

- Draw a line that passes through point M and is perpendicular to CD.
- Draw the line AB passing through the point M and perpendicular to the line just drawn in step 1. We have the line AB parallel to the line CD.

**Lesson 2: **Let ABC be a triangle whose vertex A is a right angle. Through the vertex A draw the line AX parallel to the side BC, through the vertex C draw the line CY parallel to the side AB. Two lines AX and CY intersect at point D, name pairs of parallel sides in quadrilateral ADCB

__Solution guide:__

- Use the eke to draw parallel lines following the same steps as in lesson 1.

Using eke to draw, we get quadrilateral ADCB as follows:

In quadrilateral ADCB there are:

– Pair of sides AD and BC are parallel to each other (Because AX is parallel to BC).

– Pair of sides AB and DC are parallel to each other (Because CY is parallel to BA).

**Lesson 3: **Let ABCD be a quadrilateral whose vertex angle A and vertex D are right angles (see figure).

a) Draw a line that passes through B and is parallel to side AD, intersecting side DC at point E.

b) Use an eke to check if the vertex angle E of quadrilateral BEDA has a right angle?

__Solution guide:__

- Using the eke to draw a line through B perpendicular to AB, we get a line parallel to AD and intersects DC at E.
- Use the eke to check that the vertex angle E of the quadrilateral BEDA is a right angle.

a) Draw a line through B perpendicular to AB, we get a line parallel to AD and intersects DC at E.

b) Using the test eke, we will see that the vertex angle E is a right angle.

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