Lesson Notes By Weeks and Term - Junior Secondary School 3

SUBJECT: MATHEMATICS

CLASS:  JSS 3

DATE:

TERM: 2nd TERM

 
WEEK THREE

TOPIC: Geometry

Similar Triangles

One of the following conditions is sufficient to show that two triangles are similar.

1. If two angle of one trangle are equal to two angles of the other.
2. If two pairs of sides are in the same ration and their included angles are the same.
3. If the ratios of the corresponding sides are equal.

Example

Show that ∆ABC and ∆XYZ shown below are similar and hence find sides AB and XZ. 

Solution

In ∆ABC:

< A = 180 – (32 + 38)

= 1100  

Similarly, in ∆XYZ 

0 – (1100 + 320) 

= 380
0 , < B = 0 and

0

Therefore, Triangles ABC and XYZ are similar because they are equiangular 

Hence:     AB  = AC  = BC

    XY      ZY       YZ

Subsitituting the given sides:

AB   =  25   =   35

2          XZ         7

Hence:   AB  =  35   and  25   = 35

      2         7             XZ       7

AB  =  35   and    25   = 35

 2         7               X2       7

7AB  = 2 x 35 ,       35 XZ = 25 x 7

AB      2 x 35  and     XZ =  25 x 7

               7                             35

AB = 2 x 35   and   XZ = 5cm 

Example 2:                 A

        X                  8cm

              D                         E  

          6 3/4  cm                                    4cm   

    B                        C

In the diagram shown above, line DE and BC are parallel. AE = 8cm, EC = 4cm, BD = 6 3/4  cm

1. Show that triangle ABC and ADE are similar
2. Calculate AD

Solution 

Triangle ADE and ABC are similar because they are equiangular

1. Let side AD be Xcm

AD    =    AE

AB        AC

        X    =    8

            X + 27/4          12

12X – 8x   =  54

          4x        54  =  13.5cm

             4

So X = AD = 13.5cm

READING ASSIGNMENT

Essential Mathematics Page 161

Exercise 18.3; 1-11

WEEKEND ASSIGNMENT

Objectives

1. Similar triangles are ____________   A. Equiparallel B. Equiangular C. Parallel
2. Ratio of corresponding angles must be  A. 1  B. parallel  C. constant
3.     

X    Find x

1110    320    A.  370     B. 320   C. 670       

1. If AB  = 6cm and AD = 8cm. What is the ratio of corresponding sides    A. ¾   B. 5/4    C. 4/5
2. The sum of angles in a triangle is ____ A. 3600   B. 2700  C.  1800 

Theory 

1.        P                X                   Q

                    10cm

             S            T

                        y    Find x

               Y

1.                   A

   M                    E

            D                           C              Find m        

1. 2/3cm      B