Special line segments in triangles worksheet is much useful to the kids who would like to practice problems on triangles.

Before we look at the worksheet, let us come to know some basic stuff about "Special line segments of triangles"

**Special line segments of triangles ****:**

The following are the four special line segments within a triangle.

1. Angle bisector

2. Perpendicular bisector

3. Median

4. Altitude

Angle Bisector :

The angle bisector divides an angle into two equal parts.

In the above triangle ABC, the line AD bisects the angle A.

That is <BAD = <DAC

So, AD is the angle bisector of angle A.

Similarly we can draw angle bisectors to the angles B and C.

Hence, every triangle will have three angle bisectors.

Perpendicular bisector :

The perpendicular bisector of a triangle is a line which is passing through the mid point of the side and also perpendicular to that side.

In the above triangle, the line ED is passing through the mid point of the side AB and also it is perpendicular to the side AB

So, ED is the perpendicular bisector in the above triangle.

Similarly we can draw perpendicular bisector to the sides BC and AC.

Hence, every triangle will have three perpendicular bisectors.

Median :

The median of a triangle is a line segment joining joining a vertex to the mid point of the opposite side.

In the above triangle, the line segment joining the vertex C and the mid point of AB which is D.

So, CD is the median in the above triangle.

Similarly, we can draw medians from the vertices A and B also.

Hence, every triangle will have three medians.

Altitude (Height) :

Altitude of a triangle is a line segment through a vertex and perpendicular to (That is, forming a right angle with) the opposite side which is considered to be base.

In the above triangle, the line segment AD is passing through the vertex A and perpendicular to the side BC.

So, AD is the altitude of the triangle.

Similarly, we can draw altitudes from the vertices B and C also.

Hence, every triangle will have three altitudes.

1) In the triangle ABC, angle A is divided in to equal halves by the line segment AC. What type of line segment is AC ?

2) In the triangle ABC, the line segment AD is passing through the vertex A and also perpendicular to the opposite side of the vertex A. What type of line segment is AD ?

3) In the triangle ABC, the line segment ED is not passing through any of the vertex but it is perpendicular to one of the sides of the triangle and also passing through the mid point of the same side. What type of line segment is ED ?

4) In the triangle ABC, the line segment AD is passing through the vertex A, perpendicular to the side BC and also passing through the mid point of the side BC. What type of line segment is AD ?

5) In the triangle ABC, the line segment AD joining the vertex A and the midpoint of the side BC. What type of line segment is AD ?

6) In the triangle ABC, there is a angle bisector at angle A. After the angle A is divided in to two equal halves, if each half measures 22°, find angle A.

7) In the triangle given below, AD is the angle bisector. If <B = 70° and <C = 60°, find <BAD and <DAC.

8) In the triangle given below, ED is the perpendicular bisector. If <B = 60° and <C = 70°, find angle <AED.

9) In the triangle given below, CD is the median. If <B = 60° and ADC = 120°, find <BCD.

10) In the triangle given below, AD = 4 cm and BC = 8 cm, find the area of the triangle.

**Problem 1 :**

In the triangle ABC, angle A is divided in to equal halves by the line segment AC. What type of line segment is AC ?

**Solution : **

**Given : A**ngle A is divided in to equal halves by the line segment AC.

**Only the angle bisector will divide an angle in to equal halves.**

** Hence the line segment AC is angle bisector.**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 2 :**

In the triangle ABC, the line segment AD is passing through the vertex A and also perpendicular to the opposite side of the vertex A. What type of line segment is AD ?

**Solution : **

**Given : T**he line segment AD is passing through the vertex A and also perpendicular to the opposite side of the vertex A.

**Only the altitude will pass through the vertex and perpendicular to the opposite side of the vertex. **

**Hence the line segment AD is altitude.**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 3 :**

In the triangle ABC, the line segment ED is not passing through any of the vertex but it is perpendicular to one of the sides of the triangle and also passing through the mid point of the same side. What type of line segment is ED ?

**Solution : **

**Given : The **line segment ED is not passing through any of the vertex but it is perpendicular to one of the sides of the triangle and also passing through the mid point of the same side

**Since the line segment ED is not passing through any of the vertex, it can not be altitude. **

**But ED is perpendicular to one of the sides of the triangle and also it is passing through the midpoint of the same side. **

**Hence the line segment ED is perpendicular bisector.**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 4 :**

In the triangle ABC, the line segment AD is passing through the vertex A, perpendicular to the side BC and also passing through the mid point of the side BC. What type of line segment is AD ?

**Solution : **

**Given : The **line segment AD is passing through the vertex A, perpendicular to the side BC and also passing through the mid point of the side BC

**Since the line segment AD is passing through one of the vertices vertex and perpendicular to the side BC, clearly AD is altitude. **

**But AD is also passing through the midpoint of BC. So it is also perpendicular bisector and median. **

**Hence the line segment AD is altitude, perpendicular bisector and median.**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 5 :**

In the triangle ABC, the line segment AD joining the vertex A and the midpoint of the side BC. What type of line segment is AD ?

**Solution : **

**Given : The **line segment AD joining the vertex A and the midpoint of the side BC.

**Only the median will join one of the vertices of the triangle and the mid point of the opposite side of the vertex.**

**Hence the line segment AD is median.**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 6 :**

In the triangle ABC, there is a angle bisector at angle A. After the angle A is divided in to two equal halves, if each half measures 22°, find angle A

**Solution :**

Angle A is divided in to two equal halves by the angle bisector and each half measures 22°,

Angle A = 22° + 22°

Angle A = 44°

**Hence, angle A is 44°**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 7 :**

In the triangle given below, AD is the angle bisector. If <B = 70°

and <C = 60°, find <BAD and <DAC.

**Solution :**

Sum of the angles of a triangle = 180°

<A + <B + <C = 180°

<A + 70 + 60 = 180

<A + 130 = 180

<A = 50°

Since AD is the angle bisector, it divides the angle <A = 50° in to two equal halves. That is 25° and 25°

**Hence, <BAD = 25° and <DAC = 25°**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 8 :**

In the triangle given below, ED is the perpendicular bisector. If <B = 60° and <C = 70°, find angle <AED.

**Solution :**

Sum of the angles of a triangle = 180°

<A + <B + <C = 180°

<A + 60 + 70 = 180

<A + 130 = 180

<A = 50°

In triangle AED, we have

<A + <AED + <EDA = 180°

50 + <AED + 90 = 180

<AED + 140 = 180

<AED = 40°

**Hence, <AED = 40°**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 9 :**

In the triangle given below, CD is the median. If <B = 60° and ADC = 120°, find <BCD.

**Solution :**

Given : < ADC = 120°

From the given figure, angle ADC and angle CDB together form a straight angle.

<ADC + <CDB = 180°

120° + <CDB = 180°

<CDB = 60°

In triangle BCD, we have

<B + <BCD + <CDB = 180°

60 + <BCD + 60 = 180

<BCD + 120 = 180

<BCD = 60

**Hence, <BCD = 60°**

Let us look at the next problem on "Special line segments in triangles worksheet"

**Problem 10 :**

In the triangle given below, AD = 4 cm and BC = 8 cm, find the area of the triangle.

**Solution : **

In the given figure, clearly AD is the height (altitude) and BC is the base of the triangle.

Area of the triangle = (1/2) x b x h

= (1/2) x 8 x 4

= 16 square cm.

**Hence, area of the triangle is 16 square cm. **

After having gone through the stuff given above, we hope that the students would have understood "Special line segments in triangles worksheet"

If you want to know more about "Special line segments in triangles worksheet", please click here

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**