**JSS 2 SECOND TERM BASIC TECH **

**Topic: TRIANGLE**

**INTRODUCTION**

A triangle may be defined as a plane figure contained by three straight lines, known as the sides of the triangles. One of the sides, usually the one most nearly horizontal, is identified as the base.

A triangle, as its name implies, has three angles. The two angles at the ends of the base are called base angles. The third angle, which is opposite the base, is called the vertical angle is formed is termed the vertex of the triangle.

The sum of the three angles of any triangle is 1800.

You can check this statement by drawing a triangle in any manner you like. Measure the three angles formed using a protractor. Sum the angles and confirm that they add up to 1800.

The altitude or height of a triangle is the perpendicular distance from the vertex to the base.

Triangles are classified according to the magnitude of their angles or according to the length of their side.

**i. Classification of Triangles according to Angles**

An **acute angle** triangle is one which has each of its three angles less than right angle.

A **right angled** triangle is one which has one of its as a right angle. The side of the triangle opposite the right angle is called the hypothenuse.

An **obtuse angled** triangle has one has one of its angles greater than a right angle.

**ii. Classification of Triangles according to sides**

An **equilateral **triangle is one which has its sides equal.

(Note: The three angles are also equal, each being 600.)

The sides are also equal i.e., AB = BC =AC. An isosceles triangle has two of its sides equal.

(Note: The two angles of the feet of the equal sides are also equal.)

A **scalene** triangle is one in which no side is equal to another.

**Construction of Triangles **

**(A) To construct a triangle given the length of the three sides**

i. Draw a horizontal line and mark off the base of the triangle AB.

ii. With centre A and a radius equal to the length of the side of the triangle, strike an arc.

iii. With centre B and a radius equal to the other side, strike another arc to cut the previous one at C.

iv. Join CA and CB to obtain the triangle ABC.

**(B) To construct a triangle given two sides and the included angle**

i. Draw a horizontal line and mark off one of the given sides AB.

ii. At A, construct the given included angle BAC with the aid of a protractor.

iii. With centre A and a radius equal to the other given side of the triangle, cut AC at D.

iv. Join DB to complete the required triangle ABD.

**(C) To construct an equilateral triangle using compasses**

Note: An isosceles triangle may be similarly constructed once its base and sides are given. The equilateral triangle may also be drawn using the 600 set-square.

**(D) To construct an equilateral triangle using 600 set-square**

i. Draw a horizontal line and mark off base AB equal to the given side.

ii. Slide the T-square below AB. Place the hypotenuse side of the 600 set-square on the t-square.

iii. Through A, draw AC at 600.

Reverse the set square, and through D draw BD at 600. AC and BD intersect at E to give the equilateral triangle EAB.