## Math 6 Chapter 2 Lesson 9: Triangles

## 1. Summary of theory

### 1.1. What is triangle ABC?

**Define:** Triangle ABC is a figure consisting of three line segments AB; BC; CA when three points A; B; C is not aligned.

**Sign: **

- The triangle ABC is denoted by \(\Delta ABC\).
- We also call the name and symbol of the triangle ABC as \(\Delta \)BCA, \(\Delta \)CAB, \(\Delta \)ACB, \(\Delta \)CBA, \(\Delta \)BAC .

– Three points A, B, C are the three vertices of the triangle.

– The three line segments AB, BC, CA are the three sides of the triangle

– Three angles BAC, CBA, ACB are the three angles of a triangle.

**Comment: **A triangle has: 3 sides, 3 vertices, 3 angles.

**Attention: **A point lies inside a triangle if it lies within all 3 angles of the triangle. A point that is neither inside the triangle nor on any side of the triangle is called the exterior point of the triangle.

**Eg: **For the picture below

– Point M (which lies within all three angles of the triangle) is the point inside the triangle.

– Point N (not inside the triangle, not on any side of the triangle) is the point outside the triangle) is the point lying outside the triangle (outside point of the triangle).

### 1.2. Draw triangles

**Eg: **Draw a triangle ABC, knowing three sides BC = 5cm, AB=4cm, AC=3cm.

**Colouration**

– Draw line segment BC = 5cm

– Draw an arc with center B, radius 4cm

– Draw an arc with center C, radius 3cm

– Take an intersection of the two arcs above, call that intersection A.

– Draw line segments AB, AC, we have \(\Delta \)ABC.

## 2. Illustrated exercise

**Question 1:** Draw consecutive shapes according to the following expressions:

a) Draw a triangle ABC, with AB = 4cm, BC = 4cm and CA = 4cm.

b) Draw the points M, N, and P which are the midpoints of the line segments AB, BC, CA respectively.

c) Draw another triangle MNP.

d) Read the names, vertices, angles, sides of triangles with 3 vertices taken from the points A, B, C, M, N, P.

**Solution guide**

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Draw consecutive shapes according to the following expressions:

a) Draw a triangle ABC, with AB = 2cm, BC = 2cm and CA = 2cm.

b) Draw the points M, N, and P which are the midpoints of the line segments AB, BC, CA respectively.

c) Draw another triangle MNP.

d) Read the names, vertices, angles, sides of triangles with 3 vertices taken from the points A, B, C, M, N, P.

**Verse 2:**

a) Draw triangle ABM with AB = 5cm, BM = AM = 6.5cm.

b) Draw the angle AMx that is adjacent to the angle AMB.

c) Draw triangle AMC, such that MA = MC and point C belongs to ray Mx.

d) Compare MB, MA, MC.

e) Indicate the length of the line segment BC.

f) Measure and give the measure of angle BAC.

g) Measure and indicate the length of the line segment AC.

### 3.2. Multiple choice exercises

**Question 1: **Given the following figure:

Name the triangles shown in the figure

A. \(\Delta ABM,\Delta AMC,\Delta ABC\)

B. \(\Delta AMC,\Delta ABC\)

C. \(\Delta ABM,\Delta AMC\)

D. \(\Delta AB\)

**Verse 2: **Given 5 points A, B, C, D, E of which no three points are collinear. How many triangles are there whose vertices are three of the five points above?

A. 9

B. 10

C. 8

D. 7

**Question 3: **Given the following figure:

Name the triangles that share side BC .

A. \(\Delta FBC,\Delta EBC,\Delta DBC\)

B. \(\Delta EBC,\Delta DBC,\Delta ABC\)

C. \(\Delta FBC,\Delta EBC,\)

D. \(\Delta FBC,\Delta EBC,\Delta DBC,\Delta ABC\)

**Question 4: **Given a straight line d that does not pass through O. On d take 6 distinct points A, B, C, D, E, F. How many triangles have point O as vertices and the remaining two vertices are two of six points A, B, C, D, E, F?

A. 15

B. 12

C. 6

D. 9

**Question 5: **For drawing:

Name the angles in triangle ABC

A. \(\widehat {ABM},\widehat {AMB},\widehat {BAM}\)

B. \(\widehat {ABM},\widehat {AMB},\widehat {BMA}\)

C. \(\widehat {ABC},\widehat {ACB},\widehat {BAM}\)

D. \(\widehat {ABC},\widehat {AMB},\widehat {CAM}\)

## 4. Conclusion

Through this lesson, you should know the following:

- Know the concept of triangles.
- Identify nails, sides, angles of triangles, points inside and outside the triangle.
- Know how to draw a triangle with the given lengths of three sides. Know the names and symbols of triangles

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