# Lesson Notes By Weeks and Term - Junior Secondary School 3

Geometry

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 âABC and âXYZ shown below are similar and hence find sides AB and XZ.

Solution

In âABC:

< A = 180 – (32 + 38)

= 1100

Similarly, in â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

Solution

Triangle ADE and ABC are similar because they are equiangular

1. Let side AD be Xcm

AB        AC

X    =    8

X + 27/        12

12X – 8x   =  54

4x        54  =  13.5cm

4

So X = AD = 13.5cm

Essential Mathematics Page 161

Exercise 18.3; 1-11

WEEKEND ASSIGNMENT

Objectives

X    Find x

1110    320    A.  370     B. 320   C. 670

Theory

1.        P                X                   Q

10cm

S            T

y    Find x

Y

1.                   A

M                    E

D                           C              Find m

1. 2/3cm      B