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Exercise 1:

1.

2. Lines (BE) and (CF) are perpendicular to the same line (AD) so they are parallel to each other.

Exercise 2:

Exercise 3:

Exercise 4:

Here is a figure where points A, B and C are aligned.

a. Write a construction program for this figure.

1) Construct a segment [AC] with a length of 7 cm.

2) Place point B on the segment [AC] such that AB = 3 cm.

3) Draw the lines (d1) and (d2) perpendicular to (AC) through points A and C.

4) Place the point D on the line (d1) such that AD = 4 cm .

5) Draw the segment [DB].

6) Draw the line (d3) perpendicular to [DB] through B.

7) Place the point E which is the point of intersection of the two lines (d2) and (d3) .

Exercise 5:

a. Draw a triangle ABC such that AB = 3 cm, AC = 5 cm and .

b. Place the point M on the segment [AB] such that AM = 1 cm .

c. Through M, draw the parallel to the line (BC); it intersects the line (AC) at N.

d. From M, draw the perpendicular to the line (BC); it intersects (BC) at Q.

Through N, draw the parallel to the line (MQ); it intersects (BC) at P.

a)See in red b)c)d) see diagram (Note, do not worry about point B’ which was only there to create an angle of 100° with the protractor)

e. What can we say about the lines (MQ) and (MN)?

Explain why.

They are **perpendicular **because according to the construction (MN) is parallel to (BC) and (BC) is perpendicular to (MQ).

Moreover, any perpendicular to (BC) is perpendicular to (MN) since (BC) // (MN)

// means “parallel”.

f. What can we say about the lines (NP) and (PQ)?

Explain why.

Since (NP) is parallel to (MQ), we know that (PQ) is perpendicular to (MQ) and therefore perpendicular to (NP).

(NP) and (PQ) are **perpendicular**

g. What is the nature of the quadrilateral MNPQ ?

Explain why.

Since the quadrilateral MNPQ has two opposite right angles, parallel sides. It is a **rectangle**.

Exercise 6:

Exercise 7:

Here are some of the constructs you need to get:

Exercise 8:

In each case, make the figure described and

indicate the nature of the triangle.

a. ABC is a triangle such that .

**ABC is a right triangle in C .**

b. MNP is a triangle such that MN=NP and .

**MNP is an isosceles triangle and right-angled in N .**

c. EFG is an isosceles triangle at each of its vertices.

**EFG is an equilateral triangle.**

Exercise 9:

Note that the three lines (EC), (BF) and (AG) are concurrent (all three intersect at the same point).

Exercise 10:

We have:

**CE= 6 cm and AC = 3 cm .**

## Corrected exercises on triangles and quadrilaterals in 6th grade.

After having consulted **the answers to these exercises on the construction of geometric figures with triangles and quadrilaterals **in the sixth grade, you can return to the **exercises in the sixth grade****.**

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